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->1.3334703435932325`,θ0->0.1977878793269242`,B->2.4235088904272057`,gC[0]->1.2182536477764787`,AL->-0.03284985793618467`,AH->-2.4769028477250044`,A[0]->1.3332747716030007`,A[1]->2.509056520191775`,A[2]->0.23349249124973034`,gC[1]->-0.057959196915142584`,gC[2]->0.009724404572707592`,gC[3]->-0.002793025431454722`,gC[4]->0.0009257841210436311`,gC[5]->-0.00034620961738400876`,gC[6]->0.0001367074480628476`,gC[7]->-0.00005708841894586652`,gC[8]->0.000024064384256136694`,gC[9]->-0.000010116684309320897`,gC[10]->4.024896426121343`*^-6,gC[11]->-1.4759300964074873`*^-6,gC[12]->4.6869971019692115`*^-7,gC[13]->-1.2362969368030153`*^-7,gC[14]->2.3952772823198148`*^-8,gC[15]->-2.9966672397259144`*^-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

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

datNum=Thread[{Range[0,11],Abs[Gls]((Range[Length[Gls]]-1)!)}];

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

datOurs=Chop[Abs[dFdξLowList[n1,h1][9]]/.sol1];

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

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}]
}]