path: root/post-submission work.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 12.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     94957,       2276]
NotebookOptionsPosition[     88074,       2163]
NotebookOutlinePosition[     88407,       2178]
CellTagsIndexPosition[     88364,       2175]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"\[CapitalPhi]", "[", "N_", "]"}], "[", "X_", "]"}], ":=", 
  RowBox[{
   RowBox[{"-", 
    SuperscriptBox["N", "2"]}], "+", 
   RowBox[{
    FractionBox["N", "2"], 
    RowBox[{"Tr", "[", 
     RowBox[{
      RowBox[{"Transpose", "[", "X", "]"}], ".", "X"}], "]"}]}]}]}]], "Input",\

 CellChangeTimes->{{3.793462980655712*^9, 3.793463026272648*^9}},
 CellLabel->"In[1]:=",ExpressionUUID->"aca4f188-900e-4e2f-82cb-6708cc7e7dd7"],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.793463471723394*^9, 
  3.7934634727823687`*^9}},ExpressionUUID->"2eb28450-94b1-4d41-8878-\
74ef319b339f"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"ssmat", "[", "N_", "]"}], "[", "v_", "]"}], ":=", 
  RowBox[{"FoldList", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"#1", "+", "#2"}], ",", 
       RowBox[{"Take", "[", 
        RowBox[{"v", ",", 
         RowBox[{"{", 
          RowBox[{"#1", ",", 
           RowBox[{"#1", "+", "#2", "-", "1"}]}], "}"}]}], "]"}]}], "}"}], 
     "&"}], ",", "1", ",", 
    RowBox[{"Range", "[", "N", "]"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.793463230474427*^9, 3.79346334132347*^9}},
 CellLabel->"In[7]:=",ExpressionUUID->"74ea7e40-fb7c-42ad-8f65-2bd70fc9b5c0"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"ssmat", "[", "3", "]"}], "[", 
  RowBox[{"{", 
   RowBox[{"a", ",", "b", ",", "c"}], "}"}], "]"}]], "Input",
 CellChangeTimes->{{3.793463327164769*^9, 3.793463335123438*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"4e9ad724-362c-4e7a-9eba-cdeeee19cbcf"],

Cell[BoxData[
 TemplateBox[{
  "Take","seqs",
   "\"Sequence specification (+n, -n, {+n}, {-n}, {m, n}, or {m, n, s}) \
expected at position \\!\\(\\*RowBox[{\\\"2\\\"}]\\) in \
\\!\\(\\*RowBox[{\\\"Take\\\", \\\"[\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\
\\\"a\\\", \\\",\\\", \\\"b\\\", \\\",\\\", \\\"c\\\"}], \\\"}\\\"}], \\\",\\\
\", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\\\"2\\\", \
\\\",\\\", RowBox[{\\\"{\\\", \\\"a\\\", \\\"}\\\"}]}], \\\"}\\\"}], \
\\\",\\\", RowBox[{\\\"{\\\", RowBox[{\\\"3\\\", \\\",\\\", \
RowBox[{\\\"{\\\", RowBox[{\\\"1\\\", \\\"+\\\", \\\"a\\\"}], \\\"}\\\"}]}], \
\\\"}\\\"}]}], \\\"}\\\"}]}], \\\"]\\\"}]\\).\"",2,8,4,31323197559230362610,
   "Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{{3.7934633353696213`*^9, 3.793463342933799*^9}},
 CellLabel->
  "During evaluation of \
In[8]:=",ExpressionUUID->"4e796e7b-8de1-4aff-a02c-0d0b747b2413"],

Cell[BoxData[
 TemplateBox[{
  "Take","seqs",
   "\"Sequence specification (+n, -n, {+n}, {-n}, {m, n}, or {m, n, s}) \
expected at position \\!\\(\\*RowBox[{\\\"2\\\"}]\\) in \
\\!\\(\\*RowBox[{\\\"Take\\\", \\\"[\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\
\\\"a\\\", \\\",\\\", \\\"b\\\", \\\",\\\", \\\"c\\\"}], \\\"}\\\"}], \\\",\\\
\", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \
RowBox[{\\\"4\\\", \\\",\\\", RowBox[{\\\"{\\\", RowBox[{\\\"2\\\", \
\\\"+\\\", \\\"a\\\"}], \\\"}\\\"}]}], \\\"}\\\"}], \\\",\\\", \
RowBox[{\\\"Take\\\", \\\"[\\\", RowBox[{RowBox[{\\\"{\\\", \
RowBox[{\\\"a\\\", \\\",\\\", \\\"b\\\", \\\",\\\", \\\"c\\\"}], \\\"}\\\"}], \
\\\",\\\", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\\\"2\\\", \
\\\",\\\", RowBox[{\\\"{\\\", \\\"a\\\", \\\"}\\\"}]}], \\\"}\\\"}], \
\\\",\\\", RowBox[{\\\"{\\\", RowBox[{\\\"3\\\", \\\",\\\", \
RowBox[{\\\"{\\\", RowBox[{\\\"Plus\\\", \\\"[\\\", RowBox[{\\\"\
\[LeftSkeleton]\\\", \\\"2\\\", \\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \
\\\"}\\\"}]}], \\\"}\\\"}]}], \\\"}\\\"}]}], \\\"]\\\"}]}], \\\"}\\\"}], \
\\\",\\\", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\\\"6\\\", \
\\\",\\\", RowBox[{\\\"{\\\", RowBox[{\\\"4\\\", \\\"+\\\", \\\"a\\\"}], \
\\\"}\\\"}]}], \\\"}\\\"}], \\\",\\\", RowBox[{\\\"2\\\", \\\"+\\\", RowBox[{\
\\\"Take\\\", \\\"[\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\\\"a\\\", \
\\\",\\\", \\\"b\\\", \\\",\\\", \\\"c\\\"}], \\\"}\\\"}], \\\",\\\", \
RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", RowBox[{\\\"2\\\", \\\",\\\", \
RowBox[{\\\"{\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"1\\\", \\\"\
\[RightSkeleton]\\\"}], \\\"}\\\"}]}], \\\"}\\\"}], \\\",\\\", \
RowBox[{\\\"{\\\", RowBox[{\\\"3\\\", \\\",\\\", RowBox[{\\\"{\\\", \
RowBox[{\\\"\[LeftSkeleton]\\\", \\\"1\\\", \\\"\[RightSkeleton]\\\"}], \\\"}\
\\\"}]}], \\\"}\\\"}]}], \\\"}\\\"}]}], \\\"]\\\"}]}]}], \\\"}\\\"}]}], \\\"}\
\\\"}]}], \\\"]\\\"}]\\).\"",2,8,5,31323197559230362610,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{{3.7934633353696213`*^9, 3.793463342938555*^9}},
 CellLabel->
  "During evaluation of \
In[8]:=",ExpressionUUID->"99833ccf-f7f6-4574-bc6e-56a9fa33fd14"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1", ",", 
   RowBox[{"{", 
    RowBox[{"2", ",", 
     RowBox[{"{", "a", "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"4", ",", 
       RowBox[{"{", 
        RowBox[{"2", "+", "a"}], "}"}]}], "}"}], ",", 
     RowBox[{"Take", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"2", ",", 
           RowBox[{"{", "a", "}"}]}], "}"}], ",", 
         RowBox[{"{", 
          RowBox[{"3", ",", 
           RowBox[{"{", 
            RowBox[{"1", "+", "a"}], "}"}]}], "}"}]}], "}"}]}], "]"}]}], 
    "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"7", ",", 
         RowBox[{"{", 
          RowBox[{"5", "+", "a"}], "}"}]}], "}"}], ",", 
       RowBox[{"3", "+", 
        RowBox[{"Take", "[", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"2", ",", 
              RowBox[{"{", "a", "}"}]}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3", ",", 
              RowBox[{"{", 
               RowBox[{"1", "+", "a"}], "}"}]}], "}"}]}], "}"}]}], "]"}]}]}], 
      "}"}], ",", 
     RowBox[{"Take", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{"4", ",", 
             RowBox[{"{", 
              RowBox[{"2", "+", "a"}], "}"}]}], "}"}], ",", 
           RowBox[{"Take", "[", 
            RowBox[{
             RowBox[{"{", 
              RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"{", 
                RowBox[{"2", ",", 
                 RowBox[{"{", "a", "}"}]}], "}"}], ",", 
               RowBox[{"{", 
                RowBox[{"3", ",", 
                 RowBox[{"{", 
                  RowBox[{"1", "+", "a"}], "}"}]}], "}"}]}], "}"}]}], "]"}]}],
           "}"}], ",", 
         RowBox[{"{", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{"6", ",", 
             RowBox[{"{", 
              RowBox[{"4", "+", "a"}], "}"}]}], "}"}], ",", 
           RowBox[{"2", "+", 
            RowBox[{"Take", "[", 
             RowBox[{
              RowBox[{"{", 
               RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", 
              RowBox[{"{", 
               RowBox[{
                RowBox[{"{", 
                 RowBox[{"2", ",", 
                  RowBox[{"{", "a", "}"}]}], "}"}], ",", 
                RowBox[{"{", 
                 RowBox[{"3", ",", 
                  RowBox[{"{", 
                   RowBox[{"1", "+", "a"}], "}"}]}], "}"}]}], "}"}]}], 
             "]"}]}]}], "}"}]}], "}"}]}], "]"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.793463335405059*^9, 3.7934633429439383`*^9}},
 CellLabel->"Out[8]=",ExpressionUUID->"4aada9fb-0136-4a39-9c2a-913465c6acfe"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"xx", "=", "\[IndentingNewLine]", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"0", ",", "a", ",", "b", ",", "c"}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"0", ",", "0", ",", "d", ",", "e"}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"0", ",", "0", ",", "0", ",", "f"}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}]}], 
    "\[IndentingNewLine]", "}"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.793463374110407*^9, 3.793463394189417*^9}},
 CellLabel->"In[9]:=",ExpressionUUID->"debf31e8-beab-4af1-a670-3db5979cd1c2"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"x4", "=", 
  RowBox[{"xx", "-", 
   RowBox[{"Transpose", "[", "xx", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.7934633974629793`*^9, 3.793463402821336*^9}},
 CellLabel->"In[10]:=",ExpressionUUID->"8886b158-c9fd-464d-85c7-fa6c18e364ab"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0", ",", "a", ",", "b", ",", "c"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "a"}], ",", "0", ",", "d", ",", "e"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "b"}], ",", 
     RowBox[{"-", "d"}], ",", "0", ",", "f"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "c"}], ",", 
     RowBox[{"-", "e"}], ",", 
     RowBox[{"-", "f"}], ",", "0"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.7934634032724943`*^9},
 CellLabel->"Out[10]=",ExpressionUUID->"8f8dddef-1985-4a97-a6bc-505f27bcc547"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Transpose", "[", "x4", "]"}], ".", "x4"}], "//", "Tr"}]], "Input",\

 CellChangeTimes->{{3.793463405254016*^9, 3.793463412421341*^9}},
 CellLabel->"In[11]:=",ExpressionUUID->"54e4a5a1-16be-4de6-9f0d-ce2e33df826d"],

Cell[BoxData[
 RowBox[{
  RowBox[{"2", " ", 
   SuperscriptBox["a", "2"]}], "+", 
  RowBox[{"2", " ", 
   SuperscriptBox["b", "2"]}], "+", 
  RowBox[{"2", " ", 
   SuperscriptBox["c", "2"]}], "+", 
  RowBox[{"2", " ", 
   SuperscriptBox["d", "2"]}], "+", 
  RowBox[{"2", " ", 
   SuperscriptBox["e", "2"]}], "+", 
  RowBox[{"2", " ", 
   SuperscriptBox["f", "2"]}]}]], "Output",
 CellChangeTimes->{3.793463412635048*^9},
 CellLabel->"Out[11]=",ExpressionUUID->"a214a07c-8435-4ab9-8f4c-9012e4af817a"]
}, Open  ]],

Cell[BoxData["Skew"], "Input",
 CellChangeTimes->{{3.793463029318808*^9, 3.793463043063738*^9}, {
  3.793463202738372*^9, 
  3.7934632034497747`*^9}},ExpressionUUID->"60ab5996-56b2-4116-a22b-\
4351bfe6a76c"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(", 
   RowBox[{"x3", "=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"0", ",", "a", ",", "b", ",", "d"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", "a"}], ",", "0", ",", "c"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", "b"}], ",", 
        RowBox[{"-", "c"}], ",", "0"}], "}"}]}], "}"}]}], ")"}], "//", 
  "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.793463132972478*^9, 
  3.793463166081422*^9}},ExpressionUUID->"7d739818-5a8a-4e64-8a11-\
c3eb86c80f79"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0", "a", "b"},
     {
      RowBox[{"-", "a"}], "0", "c"},
     {
      RowBox[{"-", "b"}], 
      RowBox[{"-", "c"}], "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.793463135335209*^9, 3.793463144677956*^9}},
 CellLabel->
  "Out[3]//MatrixForm=",ExpressionUUID->"5e118c38-3841-4e44-a4f4-\
4c504b5cc22c"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Tr", "[", 
  RowBox[{
   RowBox[{"Transpose", "[", "x3", "]"}], ".", "x3"}], "]"}]], "Input",
 CellChangeTimes->{{3.7934631023473177`*^9, 3.7934631552982683`*^9}},
 CellLabel->"In[4]:=",ExpressionUUID->"33d7f345-4f7e-463b-8a47-f9a31fac8992"],

Cell[BoxData[
 RowBox[{
  RowBox[{"2", " ", 
   SuperscriptBox["a", "2"]}], "+", 
  RowBox[{"2", " ", 
   SuperscriptBox["b", "2"]}], "+", 
  RowBox[{"2", " ", 
   SuperscriptBox["c", "2"]}]}]], "Output",
 CellChangeTimes->{3.79346315553784*^9},
 CellLabel->"Out[4]=",ExpressionUUID->"b8e16ebb-99fc-421d-8b9f-17c8b7116188"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate", "[", 
  RowBox[{
   RowBox[{"Exp", "[", 
    RowBox[{
     RowBox[{"-", "\[Beta]"}], " ", "n", " ", 
     SuperscriptBox["x", "2"]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "\[Infinity]"}], ",", "\[Infinity]"}], "}"}], ",", 
   RowBox[{"Assumptions", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"\[Beta]", ">", "0"}], ",", 
      RowBox[{"n", ">", "0"}]}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7934637531788597`*^9, 3.793463806724815*^9}},
 CellLabel->"In[14]:=",ExpressionUUID->"a5e5313a-3cbe-4ee7-bf9f-86d6d149c6fe"],

Cell[BoxData[
 FractionBox[
  SqrtBox["\[Pi]"], 
  SqrtBox[
   RowBox[{"n", " ", "\[Beta]"}]]]], "Output",
 CellChangeTimes->{{3.793463799306137*^9, 3.793463807151404*^9}},
 CellLabel->"Out[14]=",ExpressionUUID->"9fbd9d22-95ab-435b-9d32-a01694cee41c"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FullSimplify", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      FractionBox[
       SuperscriptBox["c", "2"], 
       RowBox[{
        SuperscriptBox["a", "2"], "+", 
        SuperscriptBox["b", "2"], "+", 
        SuperscriptBox["c", "2"]}]], "-", 
      FractionBox[
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", 
           SuperscriptBox["a", "2"]}], "-", 
          SuperscriptBox["b", "2"]}], ")"}], " ", 
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{"-", 
          SqrtBox[
           RowBox[{
            RowBox[{"-", 
             SuperscriptBox["a", "2"]}], "-", 
            SuperscriptBox["b", "2"], "-", 
            SuperscriptBox["c", "2"]}]]}]]}], 
       RowBox[{"2", " ", 
        RowBox[{"(", 
         RowBox[{
          SuperscriptBox["a", "2"], "+", 
          SuperscriptBox["b", "2"], "+", 
          SuperscriptBox["c", "2"]}], ")"}]}]], "-", 
      FractionBox[
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", 
           SuperscriptBox["a", "2"]}], "-", 
          SuperscriptBox["b", "2"]}], ")"}], " ", 
        SuperscriptBox["\[ExponentialE]", 
         SqrtBox[
          RowBox[{
           RowBox[{"-", 
            SuperscriptBox["a", "2"]}], "-", 
           SuperscriptBox["b", "2"], "-", 
           SuperscriptBox["c", "2"]}]]]}], 
       RowBox[{"2", " ", 
        RowBox[{"(", 
         RowBox[{
          SuperscriptBox["a", "2"], "+", 
          SuperscriptBox["b", "2"], "+", 
          SuperscriptBox["c", "2"]}], ")"}]}]]}], "/.", 
     RowBox[{"c", "\[Rule]", "0"}]}], "/.", 
    RowBox[{"b", "\[Rule]", "0"}]}], ",", 
   RowBox[{"Assumptions", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"a", ">", "0"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.793464485231653*^9, 3.7934645207379704`*^9}},
 CellLabel->"In[26]:=",ExpressionUUID->"c80114c3-359b-4431-b57c-41ec3ec86c28"],

Cell[BoxData[
 RowBox[{"Cos", "[", "a", "]"}]], "Output",
 CellChangeTimes->{3.793464520980328*^9},
 CellLabel->"Out[26]=",ExpressionUUID->"ecb93ba9-a956-4222-b24f-e0206d97dee4"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["a", "2"], "+", 
  SuperscriptBox["b", "2"]}]], "Input",
 CellChangeTimes->{{3.793464559625558*^9, 
  3.793464565208747*^9}},ExpressionUUID->"1e05e21d-787c-426a-9b90-\
e83b24238655"],

Cell[BoxData[
 RowBox[{"Clear", "[", "b", "]"}]], "Input",
 CellChangeTimes->{{3.7934667475081577`*^9, 3.793466752977477*^9}},
 CellLabel->"In[73]:=",ExpressionUUID->"66f37bdc-cf01-4316-9982-d4a449b28fe5"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       FractionBox[
        RowBox[{"b", " ", "c"}], 
        RowBox[{
         SuperscriptBox["a", "2"], "+", 
         SuperscriptBox["b", "2"], "+", 
         SuperscriptBox["c", "2"]}]]}], "-", 
      FractionBox[
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           RowBox[{"-", "b"}], " ", "c"}], "+", 
          RowBox[{"a", " ", 
           SqrtBox[
            RowBox[{
             RowBox[{"-", 
              SuperscriptBox["a", "2"]}], "-", 
             SuperscriptBox["b", "2"], "-", 
             SuperscriptBox["c", "2"]}]]}]}], ")"}], " ", 
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{"-", 
          SqrtBox[
           RowBox[{
            RowBox[{"-", 
             SuperscriptBox["a", "2"]}], "-", 
            SuperscriptBox["b", "2"], "-", 
            SuperscriptBox["c", "2"]}]]}]]}], 
       RowBox[{"2", " ", 
        RowBox[{"(", 
         RowBox[{
          SuperscriptBox["a", "2"], "+", 
          SuperscriptBox["b", "2"], "+", 
          SuperscriptBox["c", "2"]}], ")"}]}]], "-", 
      FractionBox[
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           RowBox[{"-", "b"}], " ", "c"}], "-", 
          RowBox[{"a", " ", 
           SqrtBox[
            RowBox[{
             RowBox[{"-", 
              SuperscriptBox["a", "2"]}], "-", 
             SuperscriptBox["b", "2"], "-", 
             SuperscriptBox["c", "2"]}]]}]}], ")"}], " ", 
        SuperscriptBox["\[ExponentialE]", 
         SqrtBox[
          RowBox[{
           RowBox[{"-", 
            SuperscriptBox["a", "2"]}], "-", 
           SuperscriptBox["b", "2"], "-", 
           SuperscriptBox["c", "2"]}]]]}], 
       RowBox[{"2", " ", 
        RowBox[{"(", 
         RowBox[{
          SuperscriptBox["a", "2"], "+", 
          SuperscriptBox["b", "2"], "+", 
          SuperscriptBox["c", "2"]}], ")"}]}]]}], "/.", 
     RowBox[{"c", "\[Rule]", "0"}]}], "/.", 
    RowBox[{"b", "\[Rule]", "0"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"a", ",", 
     RowBox[{"-", "20"}], ",", "20"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.793464222606069*^9, 3.793464305454688*^9}, {
  3.793464449270852*^9, 3.793464461038485*^9}, {3.793466655978685*^9, 
  3.7934666677943993`*^9}},
 CellLabel->"In[68]:=",ExpressionUUID->"4c3c31ca-4388-4656-980a-b8756fc51dde"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwUmnc8Vf8fx+2d7ES4xrXXRSjyOd+shkoSUtkrpJJQ2QmVNERmyCg0ZUTy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       "]]},
     Annotation[#, "Charting`Private`Tag$852617#1"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-20, 20}, {-0.9999993575792578, 0.9999999496884054}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.7934642265558367`*^9, {3.79346425859669*^9, 3.793464306101451*^9}, {
   3.7934644554334497`*^9, 3.793464461383195*^9}, 3.7934666695829*^9},
 CellLabel->"Out[68]=",ExpressionUUID->"f8286c1f-f644-4bfb-83c7-8ed63b92cbce"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", "1", ",", 
     RowBox[{"-", "1"}]}], "}"}], ".", 
   RowBox[{
    RowBox[{"MatrixExp", "[", "x3", "]"}], "[", 
    RowBox[{"[", "1", "]"}], "]"}]}], "//", "FullSimplify"}]], "Input",
 CellChangeTimes->{{3.7934641442183743`*^9, 3.793464156873516*^9}, {
  3.79346671107231*^9, 3.793466764513672*^9}},
 CellLabel->"In[76]:=",ExpressionUUID->"8bae4557-85bc-4792-906e-cdf5f9954a44"],

Cell[BoxData[
 FractionBox[
  RowBox[{
   RowBox[{
    RowBox[{"-", 
     RowBox[{"(", 
      RowBox[{"a", "+", "b", "-", "c"}], ")"}]}], " ", "c"}], "+", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox["a", "2"], "+", 
      RowBox[{"a", " ", "c"}], "+", 
      RowBox[{"b", " ", 
       RowBox[{"(", 
        RowBox[{"b", "+", "c"}], ")"}]}]}], ")"}], " ", 
    RowBox[{"Cosh", "[", 
     SqrtBox[
      RowBox[{
       RowBox[{"-", 
        SuperscriptBox["a", "2"]}], "-", 
       SuperscriptBox["b", "2"], "-", 
       SuperscriptBox["c", "2"]}]], "]"}]}], "+", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "a"}], "+", "b"}], ")"}], " ", 
    SqrtBox[
     RowBox[{
      RowBox[{"-", 
       SuperscriptBox["a", "2"]}], "-", 
      SuperscriptBox["b", "2"], "-", 
      SuperscriptBox["c", "2"]}]], " ", 
    RowBox[{"Sinh", "[", 
     SqrtBox[
      RowBox[{
       RowBox[{"-", 
        SuperscriptBox["a", "2"]}], "-", 
       SuperscriptBox["b", "2"], "-", 
       SuperscriptBox["c", "2"]}]], "]"}]}]}], 
  RowBox[{
   SuperscriptBox["a", "2"], "+", 
   SuperscriptBox["b", "2"], "+", 
   SuperscriptBox["c", "2"]}]]], "Output",
 CellChangeTimes->{{3.7934641500492496`*^9, 3.7934641572882633`*^9}, {
  3.7934667247489147`*^9, 3.793466766544986*^9}},
 CellLabel->"Out[76]=",ExpressionUUID->"8c5d5347-5047-44ec-ab4e-1d6d37a085ad"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"a", "=", 
  RowBox[{"FullSimplify", "[", 
   RowBox[{
    RowBox[{
     SuperscriptBox["r", 
      RowBox[{
       RowBox[{"n", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"n", "-", "1"}], ")"}], "/", "2"}]}], "-", "1"}]], " ", 
     RowBox[{"Exp", "[", 
      RowBox[{
       RowBox[{"-", "\[Beta]"}], " ", "n", " ", 
       SuperscriptBox["r", "2"]}], "]"}], "2", 
     RowBox[{
      RowBox[{
       SuperscriptBox["\[Pi]", 
        RowBox[{"n", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"n", "-", "1"}], ")"}], "/", "4"}]}]], "/", 
       RowBox[{"Gamma", "[", 
        RowBox[{"n", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"n", "-", "1"}], ")"}], "/", "4"}]}], "]"}]}], "/", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{
         SuperscriptBox["\[Pi]", 
          RowBox[{"1", "/", "2"}]], "/", 
         RowBox[{"Sqrt", "[", 
          RowBox[{"n", " ", "\[Beta]"}], "]"}]}], ")"}], 
       RowBox[{"n", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"n", "-", "1"}], ")"}], "/", "2"}]}]]}]}], ",", 
    RowBox[{"Assumptions", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"\[Beta]", ">", "0"}], ",", 
       RowBox[{"n", ">", "0"}]}], "}"}]}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.793465164938962*^9, 3.793465276942292*^9}, {
   3.793465394288927*^9, 3.793465415723238*^9}, {3.79346555100313*^9, 
   3.79346555531676*^9}, 3.793465637781562*^9, {3.7934657388041058`*^9, 
   3.7934657487124987`*^9}, {3.7934660943107843`*^9, 3.793466111187224*^9}, {
   3.793466158296303*^9, 3.7934661605743647`*^9}},
 CellLabel->"In[50]:=",ExpressionUUID->"e95aa855-0ec5-4b02-9a2b-7b9f8ad86b9a"],

Cell[BoxData[
 FractionBox[
  RowBox[{"2", " ", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     RowBox[{"-", "n"}], " ", 
     SuperscriptBox["r", "2"], " ", "\[Beta]"}]], " ", 
   SuperscriptBox["r", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "2"}], "+", "n"}], ")"}], " ", 
     RowBox[{"(", 
      RowBox[{"1", "+", "n"}], ")"}]}]], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"n", " ", "\[Beta]"}], ")"}], 
    RowBox[{
     FractionBox["1", "4"], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}]]}], 
  RowBox[{"Gamma", "[", 
   RowBox[{
    FractionBox["1", "4"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}], "]"}]]], "Output",
 CellChangeTimes->{{3.793465255105665*^9, 3.793465277477212*^9}, 
   3.793465453681077*^9, 3.793465555715981*^9, 3.7934656389289494`*^9, {
   3.7934657395221357`*^9, 3.793465749034925*^9}, {3.793466094794734*^9, 
   3.7934661117947063`*^9}, 3.793466161150166*^9},
 CellLabel->"Out[50]=",ExpressionUUID->"28fe16a3-13d3-4ad9-b940-beced42022e7"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"b", "=", 
   RowBox[{"Sum", "[", 
    RowBox[{
     RowBox[{"a", "/.", 
      RowBox[{"{", 
       RowBox[{"r", "\[Rule]", 
        RowBox[{
         RowBox[{"\[Pi]", "/", "2"}], "+", 
         RowBox[{"\[Pi]", " ", "m"}]}]}], "}"}]}], ",", 
     RowBox[{"{", 
      RowBox[{"m", ",", "0", ",", "5"}], "}"}]}], "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.79346630866848*^9, 3.793466387235531*^9}, {
  3.793466478960395*^9, 3.793466485768878*^9}},
 CellLabel->"In[65]:=",ExpressionUUID->"980574f0-a6f2-4bdb-9087-5c4edf46b08f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"LogLogPlot", "[", 
  RowBox[{
   RowBox[{"b", "/.", 
    RowBox[{"{", 
     RowBox[{"\[Beta]", "\[Rule]", "10"}], "}"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"n", ",", "1", ",", "100"}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.793466199858704*^9, 3.7934662491211367`*^9}, {
  3.793466488996272*^9, 3.793466499921826*^9}},
 CellLabel->"In[67]:=",ExpressionUUID->"d81a95b0-baac-41e2-85a1-56476d76e643"],

Cell[BoxData[
 TemplateBox[{
  "General","munfl",
   "\"\\!\\(\\*RowBox[{\\\"Exp\\\", \\\"[\\\", RowBox[{\\\"-\\\", \
\\\"2985.836216774226`\\\"}], \\\"]\\\"}]\\) is too small to represent as a \
normalized machine number; precision may be lost.\"",2,67,17,
   31323197559230362610,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{{3.79346649455048*^9, 3.79346650022822*^9}},
 CellLabel->
  "During evaluation of \
In[67]:=",ExpressionUUID->"0276ced0-3e05-4431-85ff-80d6cff2f239"],

Cell[BoxData[
 TemplateBox[{
  "General","munfl",
   "\"\\!\\(\\*RowBox[{\\\"Exp\\\", \\\"[\\\", RowBox[{\\\"-\\\", \
\\\"1998.7829219728292`\\\"}], \\\"]\\\"}]\\) is too small to represent as a \
normalized machine number; precision may be lost.\"",2,67,18,
   31323197559230362610,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{{3.79346649455048*^9, 3.793466500247039*^9}},
 CellLabel->
  "During evaluation of \
In[67]:=",ExpressionUUID->"683c37e9-522b-416a-9aec-0a641843f48a"],

Cell[BoxData[
 TemplateBox[{
  "General","munfl",
   "\"\\!\\(\\*RowBox[{\\\"Exp\\\", \\\"[\\\", RowBox[{\\\"-\\\", \
\\\"1209.1402861317115`\\\"}], \\\"]\\\"}]\\) is too small to represent as a \
normalized machine number; precision may be lost.\"",2,67,19,
   31323197559230362610,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{{3.79346649455048*^9, 3.793466500266004*^9}},
 CellLabel->
  "During evaluation of \
In[67]:=",ExpressionUUID->"4eb8e038-2070-460c-b6a7-fc43b0c32baf"],

Cell[BoxData[
 TemplateBox[{
  "General","stop",
   "\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"General\\\", \
\\\"::\\\", \\\"munfl\\\"}], \\\"MessageName\\\"]\\) will be suppressed \
during this calculation.\"",2,67,20,31323197559230362610,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{{3.79346649455048*^9, 3.793466500285001*^9}},
 CellLabel->
  "During evaluation of \
In[67]:=",ExpressionUUID->"be60879b-9aaf-4b71-b856-f45eacbe3f80"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwVknk0lXsXx2U856lQZMh0q2NsUCkZOs/vV4aipMicMs/Oo+GNUJnJNZUx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       "]]},
     Annotation[#, "Charting`Private`Tag$852402#1"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{9.398306502016513*^-8, -254.89001668325236`},
  CoordinatesToolOptions:>{"DisplayFunction" -> ({
      Exp[
       Part[#, 1]], 
      Exp[
       Part[#, 2]]}& ), "CopiedValueFunction" -> ({
      Exp[
       Part[#, 1]], 
      Exp[
       Part[#, 2]]}& )},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Quiet[
      Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
     Charting`ScaledFrameTicks[{Log, Exp}]}, {Quiet[
      Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
     Charting`ScaledFrameTicks[{Log, Exp}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->FrontEndValueCache[{Quiet[
      Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , Quiet[
      Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& }, {{{0., 
       FormBox["1", TraditionalForm], {0.01, 0.}, {
        AbsoluteThickness[0.1]}}, {0.6931471805599453, 
       FormBox["2", TraditionalForm], {0.01, 0.}, {
        AbsoluteThickness[0.1]}}, {1.6094379124341003`, 
       FormBox["5", TraditionalForm], {0.01, 0.}, {
        AbsoluteThickness[0.1]}}, {2.302585092994046, 
       FormBox["10", TraditionalForm], {0.01, 0.}, {
        AbsoluteThickness[0.1]}}, {2.995732273553991, 
       FormBox["20", TraditionalForm], {0.01, 0.}, {
        AbsoluteThickness[0.1]}}, {-0.6931471805599453, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {-0.5108256237659907, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {-0.35667494393873245`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {-0.2231435513142097, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {-0.10536051565782628`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {0.4054651081081644, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {1.0986122886681098`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {1.3862943611198906`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {1.791759469228055, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {1.9459101490553132`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {2.0794415416798357`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {2.1972245773362196`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {2.70805020110221, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {3.4011973816621555`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {3.6888794541139363`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {3.912023005428146, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {4.0943445622221, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {4.248495242049359, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {4.382026634673881, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {4.499809670330265, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {4.605170185988092, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {5.0106352940962555`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {5.298317366548036, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}}, {{-253.28436022934503`, 
       FormBox[
        TemplateBox[{"10", 
          RowBox[{"-", "110"}]}, "Superscript", SyntaxForm -> SuperscriptBox],
         TraditionalForm], {0.01, 0.}, {
        AbsoluteThickness[0.1]}}, {-207.2326583694641, 
       FormBox[
        TemplateBox[{"10", 
          RowBox[{"-", "90"}]}, "Superscript", SyntaxForm -> SuperscriptBox], 
        TraditionalForm], {0.01, 0.}, {
        AbsoluteThickness[0.1]}}, {-161.1809565095832, 
       FormBox[
        TemplateBox[{"10", 
          RowBox[{"-", "70"}]}, "Superscript", SyntaxForm -> SuperscriptBox], 
        TraditionalForm], {0.01, 0.}, {
        AbsoluteThickness[0.1]}}, {-115.12925464970229`, 
       FormBox[
        TemplateBox[{"10", 
          RowBox[{"-", "50"}]}, "Superscript", SyntaxForm -> SuperscriptBox], 
        TraditionalForm], {0.01, 0.}, {
        AbsoluteThickness[0.1]}}, {-69.07755278982137, 
       FormBox[
        TemplateBox[{"10", 
          RowBox[{"-", "30"}]}, "Superscript", SyntaxForm -> SuperscriptBox], 
        TraditionalForm], {0.01, 0.}, {
        AbsoluteThickness[0.1]}}, {-23.025850929940457`, 
       FormBox[
        TemplateBox[{"10", 
          RowBox[{"-", "10"}]}, "Superscript", SyntaxForm -> SuperscriptBox], 
        TraditionalForm], {0.01, 0.}, {
        AbsoluteThickness[0.1]}}, {-230.25850929940458`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {-184.20680743952366`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {-138.15510557964274`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {-92.10340371976183, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}, {-46.051701859880914`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, {
        AbsoluteThickness[0.1]}}}}]]], "Output",
 CellChangeTimes->{{3.793466220564404*^9, 3.793466249380309*^9}, {
  3.793466494667863*^9, 3.79346650031164*^9}},
 CellLabel->"Out[67]=",ExpressionUUID->"92a6d277-5c42-4f63-b117-58768a23e8fc"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FullSimplify", "[", 
  RowBox[{"a", "/.", 
   RowBox[{"r", "\[Rule]", 
    RowBox[{"\[Pi]", "/", "2"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.793466168378406*^9, 3.7934661818634033`*^9}},
 CellLabel->"In[53]:=",ExpressionUUID->"19fa357b-b8b2-42f2-86cf-c70cabcec230"],

Cell[BoxData[
 FractionBox[
  RowBox[{
   SuperscriptBox["2", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"(", 
      RowBox[{"4", "+", "n", "-", 
       SuperscriptBox["n", "2"]}], ")"}]}]], " ", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     RowBox[{"-", 
      FractionBox["1", "4"]}], " ", "n", " ", 
     SuperscriptBox["\[Pi]", "2"], " ", "\[Beta]"}]], " ", 
   SuperscriptBox["\[Pi]", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "2"}], "+", "n"}], ")"}], " ", 
     RowBox[{"(", 
      RowBox[{"1", "+", "n"}], ")"}]}]], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"n", " ", "\[Beta]"}], ")"}], 
    RowBox[{
     FractionBox["1", "4"], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}]]}], 
  RowBox[{"Gamma", "[", 
   RowBox[{
    FractionBox["1", "4"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}], "]"}]]], "Output",
 CellChangeTimes->{{3.793466174263611*^9, 3.793466182245388*^9}},
 CellLabel->"Out[53]=",ExpressionUUID->"17ffa7ee-f62f-4e9a-b461-02cd24382398"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate", "[", 
  RowBox[{"a", ",", 
   RowBox[{"{", 
    RowBox[{"r", ",", "0", ",", "\[Infinity]"}], "}"}], ",", 
   RowBox[{"Assumptions", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"\[Beta]", ">", "0"}], ",", 
      RowBox[{"n", ">", "1"}]}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.793465454645339*^9, 3.793465462602173*^9}, {
  3.793465562788645*^9, 3.793465581416975*^9}},
 CellLabel->"In[51]:=",ExpressionUUID->"ba8f198a-690c-424d-9cc7-343746fa1b85"],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{
  3.793465483432444*^9, {3.793465561747189*^9, 3.793465583809306*^9}, 
   3.793465641281439*^9, {3.793465740366543*^9, 3.793465751406748*^9}, {
   3.7934660976848183`*^9, 3.79346611407049*^9}, 3.7934661640146103`*^9},
 CellLabel->"Out[51]=",ExpressionUUID->"b1226115-e262-43fa-91ef-96afd5531fd9"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Series", "[", 
  RowBox[{"a", ",", 
   RowBox[{"{", 
    RowBox[{"\[Beta]", ",", "\[Infinity]", ",", "1"}], "}"}], ",", 
   RowBox[{"Assumptions", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"n", ">", "0"}], ",", 
      RowBox[{"\[Beta]", ">", "0"}]}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.793465280424767*^9, 3.793465297775216*^9}},
 CellLabel->"In[31]:=",ExpressionUUID->"a69d3ea3-6c53-4757-98a9-c615f36923a6"],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["2", 
   RowBox[{
    RowBox[{"-", 
     FractionBox["1", "2"]}], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "2"}], "+", "n"}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{"1", "+", "n"}], ")"}]}]], " ", 
  SuperscriptBox["\[ExponentialE]", 
   InterpretationBox[
    RowBox[{
     RowBox[{"-", 
      RowBox[{
       FractionBox["1", "4"], " ", 
       RowBox[{"(", 
        RowBox[{"n", " ", 
         SuperscriptBox["\[Pi]", "2"]}], ")"}], " ", "\[Beta]"}]}], "+", 
     InterpretationBox[
      SuperscriptBox[
       RowBox[{"O", "[", 
        FractionBox["1", "\[Beta]"], "]"}], "2"],
      SeriesData[$CellContext`\[Beta], 
       DirectedInfinity[1], {}, -1, 2, 1],
      Editable->False]}],
    SeriesData[$CellContext`\[Beta], 
     DirectedInfinity[1], {Rational[-1, 4] $CellContext`n Pi^2}, -1, 2, 1],
    Editable->False]], " ", 
  SuperscriptBox["\[Pi]", 
   RowBox[{
    FractionBox["1", "4"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}]], " ", 
  SuperscriptBox[
   RowBox[{"(", 
    RowBox[{"n", " ", "\[Beta]"}], ")"}], 
   RowBox[{
    FractionBox["1", "4"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}]], " ", 
  RowBox[{"Gamma", "[", 
   RowBox[{
    FractionBox["1", "4"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", "n"}], "]"}]}]], "Output",
 CellChangeTimes->{{3.793465287033741*^9, 3.793465298181282*^9}},
 CellLabel->"Out[31]=",ExpressionUUID->"de5bf86e-f71c-4d66-a846-9cdd3eec0bfa"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  SuperscriptBox[
   RowBox[{"(", 
    RowBox[{
     RowBox[{"6", 
      RowBox[{"s", "[", 
       RowBox[{"1", ",", "1", ",", "1"}], "]"}]}], "-", 
     RowBox[{"s", "[", 
      RowBox[{"0", ",", "1", ",", "1"}], "]"}], "-", 
     RowBox[{"s", "[", 
      RowBox[{"1", ",", "0", ",", "1"}], "]"}], "-", 
     RowBox[{"s", "[", 
      RowBox[{"1", ",", "1", ",", "0"}], "]"}], "-", 
     RowBox[{"s", "[", 
      RowBox[{"2", ",", "1", ",", "1"}], "]"}], "-", 
     RowBox[{"s", "[", 
      RowBox[{"1", ",", "2", ",", "1"}], "]"}], "-", 
     RowBox[{"s", "[", 
      RowBox[{"1", ",", "1", ",", "2"}], "]"}]}], ")"}], "2"], "//", 
  "Expand"}]], "Input",
 CellChangeTimes->{{3.793536642823517*^9, 3.793536686774036*^9}},
 CellLabel->"In[79]:=",ExpressionUUID->"76a5a6bf-8a98-4d15-942b-df42914ad53b"],

Cell[BoxData["7"], "Input",
 CellChangeTimes->{
  3.7936296303941603`*^9},ExpressionUUID->"56f2956b-d07d-4363-8656-\
bbcfe2c5f5f3"],

Cell[BoxData[
 RowBox[{
  SuperscriptBox[
   RowBox[{"s", "[", 
    RowBox[{"0", ",", "1", ",", "1"}], "]"}], "2"], "+", "cl", "+", 
  SuperscriptBox[
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "0", ",", "1"}], "]"}], "2"], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"0", ",", "1", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "0"}], "]"}]}], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "0", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "0"}], "]"}]}], "+", 
  SuperscriptBox[
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "0"}], "]"}], "2"], "-", 
  RowBox[{"12", " ", 
   RowBox[{"s", "[", 
    RowBox[{"0", ",", "1", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "1"}], "]"}]}], "-", 
  RowBox[{"12", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "0", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "1"}], "]"}]}], "-", 
  RowBox[{"12", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "0"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "1"}], "]"}]}], "+", 
  RowBox[{"36", " ", 
   SuperscriptBox[
    RowBox[{"s", "[", 
     RowBox[{"1", ",", "1", ",", "1"}], "]"}], "2"]}], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"0", ",", "1", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "2"}], "]"}]}], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "0", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "2"}], "]"}]}], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "0"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "2"}], "]"}]}], "-", 
  RowBox[{"12", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "2"}], "]"}]}], "+", 
  SuperscriptBox[
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "2"}], "]"}], "2"], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"0", ",", "1", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "0", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "0"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "-", 
  RowBox[{"12", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "2"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "+", 
  SuperscriptBox[
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "2", ",", "1"}], "]"}], "2"], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"0", ",", "1", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "0", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "0"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "-", 
  RowBox[{"12", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "1", ",", "2"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "+", 
  RowBox[{"2", " ", 
   RowBox[{"s", "[", 
    RowBox[{"1", ",", "2", ",", "1"}], "]"}], " ", 
   RowBox[{"s", "[", 
    RowBox[{"2", ",", "1", ",", "1"}], "]"}]}], "+", 
  SuperscriptBox[
   RowBox[{"s", "[", 
    RowBox[{"2", ",", "1", ",", "1"}], "]"}], "2"]}]], "Input",
 CellChangeTimes->{{3.7935394747462997`*^9, 
  3.7935394748445168`*^9}},ExpressionUUID->"5ab2d411-f76c-439c-b4a8-\
69e4391bfc67"],

Cell[BoxData[
 RowBox[{
  RowBox[{"A", "=", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"1", "-", 
     RowBox[{
      FractionBox[
       RowBox[{"8", "g"}], 
       SuperscriptBox["b", "2"]], 
      RowBox[{"\[Eta]", "[", "x", "]"}], "\[Delta]Fo\[Delta]\[Eta]"}]}], 
    "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.793741067148281*^9, 3.7937411136426697`*^9}},
 CellLabel->"In[80]:=",ExpressionUUID->"fead141c-7cf2-478d-a297-838bebe09fc8"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Series", "[", 
  RowBox[{
   RowBox[{"Sqrt", "[", 
    RowBox[{"1", "-", 
     RowBox[{
      FractionBox[
       RowBox[{"8", "g"}], 
       SuperscriptBox["b", "2"]], 
      RowBox[{"\[Eta]", "[", "x", "]"}], "\[Delta]Fo\[Delta]\[Eta]"}]}], 
    "]"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"\[Eta]", "[", "x", "]"}], ",", "0", ",", "1"}], "}"}]}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.793743846800037*^9, 3.793743856039771*^9}},
 CellLabel->"In[98]:=",ExpressionUUID->"f60f6ced-d698-434d-b1b6-259a8d3625bf"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"1", "-", 
   FractionBox[
    RowBox[{"4", " ", 
     RowBox[{"(", 
      RowBox[{"g", " ", "\[Delta]Fo\[Delta]\[Eta]"}], ")"}], " ", 
     RowBox[{"\[Eta]", "[", "x", "]"}]}], 
    SuperscriptBox["b", "2"]], "+", 
   InterpretationBox[
    SuperscriptBox[
     RowBox[{"O", "[", 
      RowBox[{"\[Eta]", "[", "x", "]"}], "]"}], "2"],
    SeriesData[
     $CellContext`\[Eta][$CellContext`x], 0, {}, 0, 2, 1],
    Editable->False]}],
  SeriesData[
   $CellContext`\[Eta][$CellContext`x], 0, {
   1, (-4) $CellContext`b^(-2) $CellContext`g $CellContext`\[Delta]Fo\[Delta]\
\[Eta]}, 0, 2, 1],
  Editable->False]], "Output",
 CellChangeTimes->{3.793743859432831*^9},
 CellLabel->"Out[98]=",ExpressionUUID->"ce625025-4360-455f-82b5-b9530ae4d111"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Series", "[", 
  RowBox[{
   RowBox[{
    FractionBox[
     SuperscriptBox["b", "2"], 
     RowBox[{"4", "g"}]], 
    RowBox[{"(", 
     RowBox[{"A", "-", 
      SuperscriptBox["A", "2"]}], ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"\[Eta]", "[", "x", "]"}], ",", "0", ",", "1"}], "}"}]}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.793741117161496*^9, 3.7937411420266447`*^9}},
 CellLabel->"In[81]:=",ExpressionUUID->"16de18cb-0c52-4dab-9a12-e27dcf2d6fc9"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{
   RowBox[{"\[Delta]Fo\[Delta]\[Eta]", " ", 
    RowBox[{"\[Eta]", "[", "x", "]"}]}], "+", 
   InterpretationBox[
    SuperscriptBox[
     RowBox[{"O", "[", 
      RowBox[{"\[Eta]", "[", "x", "]"}], "]"}], "2"],
    SeriesData[
     $CellContext`\[Eta][$CellContext`x], 0, {}, 1, 2, 1],
    Editable->False]}],
  SeriesData[
   $CellContext`\[Eta][$CellContext`x], 
   0, {$CellContext`\[Delta]Fo\[Delta]\[Eta]}, 1, 2, 1],
  Editable->False]], "Output",
 CellChangeTimes->{3.793741142658823*^9},
 CellLabel->"Out[81]=",ExpressionUUID->"5c86022f-2a97-426d-a105-27ca644556d3"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"cc", "=", 
  RowBox[{"CC", "-", 
   RowBox[{"b", 
    RowBox[{"(", 
     RowBox[{"2", "-", "A"}], ")"}], 
    RowBox[{"(", 
     FractionBox["1", 
      RowBox[{"b", " ", "A", " ", "\[Chi]"}]]}]}]}]}]], "Input",
 CellChangeTimes->{{3.793742041190386*^9, 
  3.793742111131962*^9}},ExpressionUUID->"b204065d-c0d3-474e-bf46-\
960ca97915f9"],

Cell[BoxData[
 RowBox[{"Clear", "[", "A", "]"}]], "Input",
 CellChangeTimes->{{3.793742928617783*^9, 3.793742934416638*^9}},
 CellLabel->"In[82]:=",ExpressionUUID->"e6e51249-1961-4ba0-8491-cc8826f3a222"],

Cell[BoxData[
 RowBox[{"A", "[", "g"}]], "Input",
 CellChangeTimes->{{3.793742935137989*^9, 
  3.7937429381919527`*^9}},ExpressionUUID->"a1f9a74f-6349-479f-a0d8-\
3afa27dbc2cf"],

Cell[BoxData[
 RowBox[{"CCC", "[", 
  RowBox[{"CC_", ",", "b_", ",", "g_", ","}]}]], "Input",
 CellChangeTimes->{{3.793742911774315*^9, 
  3.793742922296541*^9}},ExpressionUUID->"2d175ba3-8b08-40f4-9f18-\
393040950671"],

Cell[BoxData[
 RowBox[{"FourierTransform", "[", 
  RowBox[{
   RowBox[{"1", "-", 
    FractionBox[
     RowBox[{"4", " ", 
      RowBox[{"(", 
       RowBox[{"g", " ", "\[Delta]Fo\[Delta]\[Eta]"}], ")"}], " ", 
      RowBox[{"\[Eta]", "[", "x", "]"}]}], 
     SuperscriptBox["b", "2"]]}], ","}]}]], "Input",
 CellChangeTimes->{{3.7937439219808197`*^9, 
  3.7937439253542013`*^9}},ExpressionUUID->"f35dc126-7704-4357-98fe-\
523e0d2f75a7"],

Cell[BoxData[
 RowBox[{"A", "=", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"Sqrt", "[", 
      RowBox[{"1", "-", 
       RowBox[{
        FractionBox[
         RowBox[{"8", "g"}], 
         SuperscriptBox["b", "2"]], 
        RowBox[{"\[Eta]", "[", "x", "]"}], 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"2", " ", "g", " ", 
           SuperscriptBox[
            RowBox[{"\[Epsilon]", "[", "x", "]"}], "2"], 
           RowBox[{"\[Eta]", "[", "x", "]"}]}], "-", 
          RowBox[{"b", " ", 
           RowBox[{"\[Epsilon]", "[", "x", "]"}]}]}], ")"}]}]}], "]"}], "/.", 
     
     RowBox[{"ss", "[", 
      RowBox[{"[", "1", "]"}], "]"}]}], "/.", 
    RowBox[{
     RowBox[{"\[Eta]", "[", "x", "]"}], "\[Rule]", 
     RowBox[{"\[Eta]s", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{"qs", " ", "x"}], "]"}]}]}]}], "//", "Simplify"}]}]], "Input",
 CellChangeTimes->{{3.793743184168146*^9, 3.793743186360269*^9}, {
  3.793743225022057*^9, 3.79374323424545*^9}, {3.793743279128126*^9, 
  3.793743292535133*^9}, {3.793743365160321*^9, 3.79374340324955*^9}, {
  3.793743451180779*^9, 3.7937434597540073`*^9}, {3.793743495073674*^9, 
  3.793743544284822*^9}},
 CellLabel->"In[91]:=",ExpressionUUID->"86367330-ecad-4848-a0ba-bdf293b66e9d"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"AA", "=", 
  SqrtBox[
   FractionBox[
    RowBox[{"1", "+", 
     RowBox[{"12", " ", "b", " ", 
      SuperscriptBox[
       RowBox[{"Cos", "[", 
        RowBox[{"qs", " ", "x"}], "]"}], "2"]}], "+", 
     RowBox[{"4", " ", 
      SuperscriptBox["b", "2"], 
      SuperscriptBox[
       RowBox[{"Cos", "[", 
        RowBox[{"qs", " ", "x"}], "]"}], "4"]}]}], 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"1", "+", 
       RowBox[{"2", " ", "b", " ", 
        SuperscriptBox[
         RowBox[{"Cos", "[", 
          RowBox[{"qs", " ", "x"}], "]"}], "2"]}]}], ")"}], "2"]]]}]], "Input",
 CellChangeTimes->{{3.793743642172892*^9, 3.793743771520555*^9}},
 CellLabel->"In[96]:=",ExpressionUUID->"e00b5722-fae6-4282-a0c0-7c74db5258e3"],

Cell[BoxData[
 SqrtBox[
  FractionBox[
   RowBox[{"1", "+", 
    RowBox[{"12", " ", "b", " ", 
     SuperscriptBox[
      RowBox[{"Cos", "[", 
       RowBox[{"qs", " ", "x"}], "]"}], "2"]}], "+", 
    RowBox[{"4", " ", 
     SuperscriptBox["b", "2"], " ", 
     SuperscriptBox[
      RowBox[{"Cos", "[", 
       RowBox[{"qs", " ", "x"}], "]"}], "4"]}]}], 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"1", "+", 
      RowBox[{"2", " ", "b", " ", 
       SuperscriptBox[
        RowBox[{"Cos", "[", 
         RowBox[{"qs", " ", "x"}], "]"}], "2"]}]}], ")"}], "2"]]]], "Output",
 CellChangeTimes->{{3.793743748383366*^9, 3.793743772054668*^9}},
 CellLabel->"Out[96]=",ExpressionUUID->"acca43d1-2cf7-4c66-8f61-f765de6fa91f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FourierTransform", "[", 
  RowBox[{"AA", ",", "x", ",", "k", ",", 
   RowBox[{"Assumptions", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"b", ">", "0"}], ",", 
      RowBox[{"k", ">", "0"}], ",", 
      RowBox[{"qs", ">", "0"}]}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7937435458307056`*^9, 3.793743551747511*^9}, {
  3.7937437747541113`*^9, 3.7937437845120173`*^9}},
 CellLabel->"In[97]:=",ExpressionUUID->"0c450611-0015-4363-aeb9-daa06cff2241"],

Cell[BoxData["$Aborted"], "Output",
 CellChangeTimes->{3.793743633712516*^9, 3.793743858452667*^9},
 CellLabel->"Out[97]=",ExpressionUUID->"45be489a-043b-499f-bfbc-dadd66a9398a"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"Convolve", "[", 
  RowBox[{
   FractionBox["1", 
    RowBox[{
     RowBox[{"d", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{
         SuperscriptBox["qs", "2"], "-", 
         SuperscriptBox["q", "2"]}], ")"}], "2"]}], "+", 
     "\[CapitalDelta]r"}]], ",", 
   RowBox[{"Sqrt", "[", 
    RowBox[{"1", "-", 
     FractionBox[
      RowBox[{"8", "g"}], 
      SuperscriptBox["b", "2"]]}]}]}]}]], "Input",
 CellChangeTimes->{{3.793743101140671*^9, 
  3.793743172813489*^9}},ExpressionUUID->"b8eeb8b8-eb37-49ca-9ce4-\
c9bfc4c7af57"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ss", "=", 
  RowBox[{"Solve", "[", 
   RowBox[{
    RowBox[{"0", "==", 
     RowBox[{
      RowBox[{"CC", " ", 
       RowBox[{"\[Epsilon]", "[", "x", "]"}]}], "-", 
      RowBox[{"b", " ", 
       RowBox[{"\[Eta]", "[", "x", "]"}]}], "+", 
      RowBox[{"2", " ", "g", " ", 
       RowBox[{"\[Epsilon]", "[", "x", "]"}], " ", 
       SuperscriptBox[
        RowBox[{"\[Eta]", "[", "x", "]"}], "2"]}]}]}], ",", 
    RowBox[{"\[Epsilon]", "[", "x", "]"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.7937433173696737`*^9, 3.793743362030386*^9}},
 CellLabel->"In[84]:=",ExpressionUUID->"7f8d0483-ea86-4a53-88fb-5f6501e09115"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"\[Epsilon]", "[", "x", "]"}], "\[Rule]", 
    FractionBox[
     RowBox[{"b", " ", 
      RowBox[{"\[Eta]", "[", "x", "]"}]}], 
     RowBox[{"CC", "+", 
      RowBox[{"2", " ", "g", " ", 
       SuperscriptBox[
        RowBox[{"\[Eta]", "[", "x", "]"}], "2"]}]}]]}], "}"}], 
  "}"}]], "Output",
 CellChangeTimes->{{3.793743357437993*^9, 3.793743362322541*^9}},
 CellLabel->"Out[84]=",ExpressionUUID->"475ec955-d0ca-4d2e-aea6-c5be3d43ec81"]
}, Open  ]]
},
WindowSize->{954, 1055},
WindowMargins->{{Automatic, 3}, {3, Automatic}},
FrontEndVersion->"12.0 for Linux x86 (64-bit) (April 8, 2019)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 474, 14, 49, "Input",ExpressionUUID->"aca4f188-900e-4e2f-82cb-6708cc7e7dd7"],
Cell[1035, 36, 154, 3, 31, "Input",ExpressionUUID->"2eb28450-94b1-4d41-8878-74ef319b339f"],
Cell[1192, 41, 639, 18, 31, "Input",ExpressionUUID->"74ea7e40-fb7c-42ad-8f65-2bd70fc9b5c0"],
Cell[CellGroupData[{
Cell[1856, 63, 287, 6, 31, "Input",ExpressionUUID->"4e9ad724-362c-4e7a-9eba-cdeeee19cbcf"],
Cell[2146, 71, 921, 17, 23, "Message",ExpressionUUID->"4e796e7b-8de1-4aff-a02c-0d0b747b2413"],
Cell[3070, 90, 2214, 34, 43, "Message",ExpressionUUID->"99833ccf-f7f6-4574-bc6e-56a9fa33fd14"],
Cell[5287, 126, 3189, 97, 105, "Output",ExpressionUUID->"4aada9fb-0136-4a39-9c2a-913465c6acfe"]
}, Open  ]],
Cell[8491, 226, 734, 18, 170, "Input",ExpressionUUID->"debf31e8-beab-4af1-a670-3db5979cd1c2"],
Cell[CellGroupData[{
Cell[9250, 248, 259, 5, 31, "Input",ExpressionUUID->"8886b158-c9fd-464d-85c7-fa6c18e364ab"],
Cell[9512, 255, 618, 18, 35, "Output",ExpressionUUID->"8f8dddef-1985-4a97-a6bc-505f27bcc547"]
}, Open  ]],
Cell[CellGroupData[{
Cell[10167, 278, 260, 6, 31, "Input",ExpressionUUID->"54e4a5a1-16be-4de6-9f0d-ce2e33df826d"],
Cell[10430, 286, 499, 15, 37, "Output",ExpressionUUID->"a214a07c-8435-4ab9-8f4c-9012e4af817a"]
}, Open  ]],
Cell[10944, 304, 207, 4, 31, "Input",ExpressionUUID->"60ab5996-56b2-4116-a22b-4351bfe6a76c"],
Cell[CellGroupData[{
Cell[11176, 312, 574, 18, 31, "Input",ExpressionUUID->"7d739818-5a8a-4e64-8a11-c3eb86c80f79"],
Cell[11753, 332, 741, 23, 83, "Output",ExpressionUUID->"5e118c38-3841-4e44-a4f4-4c504b5cc22c"]
}, Open  ]],
Cell[CellGroupData[{
Cell[12531, 360, 265, 5, 31, "Input",ExpressionUUID->"33d7f345-4f7e-463b-8a47-f9a31fac8992"],
Cell[12799, 367, 323, 9, 37, "Output",ExpressionUUID->"b8e16ebb-99fc-421d-8b9f-17c8b7116188"]
}, Open  ]],
Cell[CellGroupData[{
Cell[13159, 381, 613, 16, 39, "Input",ExpressionUUID->"a5e5313a-3cbe-4ee7-bf9f-86d6d149c6fe"],
Cell[13775, 399, 251, 6, 62, "Output",ExpressionUUID->"9fbd9d22-95ab-435b-9d32-a01694cee41c"]
}, Open  ]],
Cell[CellGroupData[{
Cell[14063, 410, 1943, 59, 108, "Input",ExpressionUUID->"c80114c3-359b-4431-b57c-41ec3ec86c28"],
Cell[16009, 471, 178, 3, 35, "Output",ExpressionUUID->"ecb93ba9-a956-4222-b24f-e0206d97dee4"]
}, Open  ]],
Cell[16202, 477, 223, 6, 33, "Input",ExpressionUUID->"1e05e21d-787c-426a-9b90-e83b24238655"],
Cell[16428, 485, 205, 3, 31, "Input",ExpressionUUID->"66f37bdc-cf01-4316-9982-d4a449b28fe5"],
Cell[CellGroupData[{
Cell[16658, 492, 2445, 74, 115, "Input",ExpressionUUID->"4c3c31ca-4388-4656-980a-b8756fc51dde"],
Cell[19106, 568, 30019, 511, 238, "Output",ExpressionUUID->"f8286c1f-f644-4bfb-83c7-8ed63b92cbce"]
}, Open  ]],
Cell[CellGroupData[{
Cell[49162, 1084, 452, 11, 31, "Input",ExpressionUUID->"8bae4557-85bc-4792-906e-cdf5f9954a44"],
Cell[49617, 1097, 1376, 45, 71, "Output",ExpressionUUID->"8c5d5347-5047-44ec-ab4e-1d6d37a085ad"]
}, Open  ]],
Cell[CellGroupData[{
Cell[51030, 1147, 1713, 48, 71, "Input",ExpressionUUID->"e95aa855-0ec5-4b02-9a2b-7b9f8ad86b9a"],
Cell[52746, 1197, 1154, 33, 76, "Output",ExpressionUUID->"28fe16a3-13d3-4ad9-b940-beced42022e7"]
}, Open  ]],
Cell[53915, 1233, 564, 15, 31, "Input",ExpressionUUID->"980574f0-a6f2-4bdb-9087-5c4edf46b08f"],
Cell[CellGroupData[{
Cell[54504, 1252, 482, 11, 31, "Input",ExpressionUUID->"d81a95b0-baac-41e2-85a1-56476d76e643"],
Cell[54989, 1265, 501, 11, 23, "Message",ExpressionUUID->"0276ced0-3e05-4431-85ff-80d6cff2f239"],
Cell[55493, 1278, 503, 11, 23, "Message",ExpressionUUID->"683c37e9-522b-416a-9aec-0a641843f48a"],
Cell[55999, 1291, 503, 11, 23, "Message",ExpressionUUID->"4eb8e038-2070-460c-b6a7-fc43b0c32baf"],
Cell[56505, 1304, 469, 10, 23, "Message",ExpressionUUID->"be60879b-9aaf-4b71-b856-f45eacbe3f80"],
Cell[56977, 1316, 11646, 238, 228, "Output",ExpressionUUID->"92a6d277-5c42-4f63-b117-58768a23e8fc"]
}, Open  ]],
Cell[CellGroupData[{
Cell[68660, 1559, 295, 6, 31, "Input",ExpressionUUID->"19fa357b-b8b2-42f2-86cf-c70cabcec230"],
Cell[68958, 1567, 1165, 37, 77, "Output",ExpressionUUID->"17ffa7ee-f62f-4e9a-b461-02cd24382398"]
}, Open  ]],
Cell[CellGroupData[{
Cell[70160, 1609, 509, 12, 31, "Input",ExpressionUUID->"ba8f198a-690c-424d-9cc7-343746fa1b85"],
Cell[70672, 1623, 345, 5, 35, "Output",ExpressionUUID->"b1226115-e262-43fa-91ef-96afd5531fd9"]
}, Open  ]],
Cell[CellGroupData[{
Cell[71054, 1633, 463, 11, 31, "Input",ExpressionUUID->"a69d3ea3-6c53-4757-98a9-c615f36923a6"],
Cell[71520, 1646, 1608, 51, 56, "Output",ExpressionUUID->"de5bf86e-f71c-4d66-a846-9cdd3eec0bfa"]
}, Open  ]],
Cell[73143, 1700, 825, 22, 33, "Input",ExpressionUUID->"76a5a6bf-8a98-4d15-942b-df42914ad53b"],
Cell[73971, 1724, 131, 3, 31, "Input",ExpressionUUID->"56f2956b-d07d-4363-8656-bbcfe2c5f5f3"],
Cell[74105, 1729, 4309, 126, 176, InheritFromParent,ExpressionUUID->"5ab2d411-f76c-439c-b4a8-69e4391bfc67"],
Cell[78417, 1857, 439, 12, 50, "Input",ExpressionUUID->"fead141c-7cf2-478d-a297-838bebe09fc8"],
Cell[CellGroupData[{
Cell[78881, 1873, 550, 16, 50, "Input",ExpressionUUID->"f60f6ced-d698-434d-b1b6-259a8d3625bf"],
Cell[79434, 1891, 787, 22, 55, "Output",ExpressionUUID->"ce625025-4360-455f-82b5-b9530ae4d111"]
}, Open  ]],
Cell[CellGroupData[{
Cell[80258, 1918, 496, 15, 56, "Input",ExpressionUUID->"16de18cb-0c52-4dab-9a12-e27dcf2d6fc9"],
Cell[80757, 1935, 619, 17, 37, "Output",ExpressionUUID->"5c86022f-2a97-426d-a105-27ca644556d3"]
}, Open  ]],
Cell[81391, 1955, 361, 11, 50, "Input",ExpressionUUID->"b204065d-c0d3-474e-bf46-960ca97915f9"],
Cell[81755, 1968, 203, 3, 31, "Input",ExpressionUUID->"e6e51249-1961-4ba0-8491-cc8826f3a222"],
Cell[81961, 1973, 177, 4, 31, "Input",ExpressionUUID->"a1f9a74f-6349-479f-a0d8-3afa27dbc2cf"],
Cell[82141, 1979, 219, 5, 31, "Input",ExpressionUUID->"2d175ba3-8b08-40f4-9f18-393040950671"],
Cell[82363, 1986, 437, 12, 51, "Input",ExpressionUUID->"f35dc126-7704-4357-98fe-523e0d2f75a7"],
Cell[82803, 2000, 1260, 33, 50, "Input",ExpressionUUID->"86367330-ecad-4848-a0ba-bdf293b66e9d"],
Cell[CellGroupData[{
Cell[84088, 2037, 762, 22, 73, InheritFromParent,ExpressionUUID->"e00b5722-fae6-4282-a0c0-7c74db5258e3"],
Cell[84853, 2061, 726, 21, 75, "Output",ExpressionUUID->"acca43d1-2cf7-4c66-8f61-f765de6fa91f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[85616, 2087, 496, 11, 31, "Input",ExpressionUUID->"0c450611-0015-4363-aeb9-daa06cff2241"],
Cell[86115, 2100, 178, 2, 35, "Output",ExpressionUUID->"45be489a-043b-499f-bfbc-dadd66a9398a"]
}, Open  ]],
Cell[86308, 2105, 568, 19, 56, "Input",ExpressionUUID->"b8eeb8b8-eb37-49ca-9ce4-c9bfc4c7af57"],
Cell[CellGroupData[{
Cell[86901, 2128, 646, 16, 39, "Input",ExpressionUUID->"7f8d0483-ea86-4a53-88fb-5f6501e09115"],
Cell[87550, 2146, 508, 14, 58, "Output",ExpressionUUID->"475ec955-d0ca-4d2e-aea6-c5be3d43ec81"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)