Get["~/doc/research/first_order_singularities/mma/schofield.wl"]

n9=2;
F9=RF[n9];
h9=h[15];

n1=2;
F1=RF[n1];
h1=h[0];
sol1={θc->1.1942649631944824`,θ0->0.1980115286480415`,B->8.55266640049003`,gC[0]->1.1942649631944824`,AL->-0.09823515561347546`,AH->-2.3836528485084885`,A[0]->1.0766637996073516`,A[1]->2.0038100879767504`,A[2]->0.22823495175053052`};

sol9={θc->1.3334703412536566`,θ0->0.19778787932056896`,B->2.423508930724686`,gC[0]->1.2182536469166905`,AL->-0.032849858698944676`,AH->-2.476902848020555`,A[0]->1.3332747682033883`,A[1]->2.5090565130203157`,A[2]->0.23349249078258508`,gC[1]->-0.05795919615164437`,gC[2]->0.009724404457489885`,gC[3]->-0.0027930254001640054`,gC[4]->0.0009257841098320665`,gC[5]->-0.0003462096131004199`,gC[6]->0.00013670744619527473`,gC[7]->-0.000057088418113155406`,gC[8]->0.000024064383846786254`,gC[9]->-0.000010116684104855923`,gC[10]->4.024896321935335`*^-6,gC[11]->-1.4759300475764031`*^-6,gC[12]->4.686996899926149`*^-7,gC[13]->-1.2362968704699286`*^-7,gC[14]->2.395277120268058`*^-8,gC[15]->-2.99666705183393`*^-9};

θ0Cas=(Sqrt[1.16951]);
hCas[θ_]:=h0(1-((θ^2)/((θ0Cas)^2)))θ(1-0.222389 (θ^2)-0.043547 (θ^4)-0.014809 (θ^6)-0.007168 (θ^8))

coeffCas[n_]:=NestList[ddξ[hCas],m0 (θ/((((θ^2)-1))^(1/8))),n]/.θ->θ0Cas

coeffCasMid[n_]:=NestList[ddη[hCas],m0 (θ/((hCas[θ])^(1/δ[2]))),n]/.θ->1

datNum[[2]]

m0rule=Solve[coeffCas[1]==datNum[[2;;3,2]],{m0,h0}][[1]]

m0/((hCas[1])^15)/.m0rule

Head[Gls[[1]]]

coeffCasMid[5]/Range[0,5]!/.m0rule

datNum=Thread[{Range[0,11],Gls}];

Export["~/doc/research/first_order_singularities/paper/data/glow_series_numeric.dat",{#1,If[Head[#2]===Around,#2["Value"],#2],If[Head[#2]===Around,#2["Uncertainty"],0]}&@@@datNum]

datCas=NestList[ddξ[hCas],m0 (θ/((((θ^2)-1))^(1/8))),10]/.θ->θ0Cas/.m0rule

datOurs=dFdξLowList[n1,h1][9]/.sol1;

Export["~/doc/research/first_order_singularities/paper/data/glow_series_ours_0.dat",Table[{i,Chop@datOurs[[i+1]]/i!},{i,0,Length[datOurs]-1}]]

Export["~/doc/research/first_order_singularities/paper/data/glow_series_caselle.dat",Table[{i,datCas[[i]]["Value"]/i!},{i,1,Length[datCas]}]]

ListLogPlot[{
datNum,Abs@datCas,Thread[{Range[0,Length[datOurs]-1],datOurs}]
}]

Export["~/doc/research/first_order_singularities/paper/data/Glow_series_numeric

datNum

convNum=Table[{i,#[[i]]/i!},{i,2,Length[#]}]&@Abs[Rest@datNum[[All,2]]]

ListPlot[{
Table[{1/i,#[[i]]/#[[i-1]]/i},{i,2,Length[#]}]&@Abs[Rest@datNum[[All,2]]],
Table[{1/i,#[[i]]/#[[i-1]]/i},{i,2,Length[#]}]&@Abs[datCas],
Table[{1/i,#[[i]]/#[[i-1]]/i},{i,2,Length[#]}]&@Rest[datOurs]
},PlotRange->{{0,0.5},All}]

datOurs=Chop[Abs[dFdξHighList[n1,h1][12]]/.sol1];

datNumHigh=Thread[{Range[0,Length[Ghs]-1],Abs[Ghs]((Range[Length[Ghs]]-1)!)}];

datCasHigh=NestList[ddξ[hCas],m0 (θ/(((1-(θ^2)))^(1/8))),11]/.θ->0/.m0rule

ListLogPlot[{
Abs@datNumHigh,Abs@datCasHigh,Thread[{Range[0,Length[datOurs]-1],datOurs}]
}]