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i0f_asympt

Function i0f_asympt 

Source
fn i0f_asympt(x: f32) -> f32
Expand description

Asymptotic expansion for I0.

Computes: sqrt(x) * exp(-x) * I0(x) = Pn(1/x)/Qn(1/x) hence: I0(x) = Pn(1/x)/Qm(1/x)*exp(x)/sqrt(x)

Generated by Mathematica:

<<FunctionApproximations`
ClearAll["Global`*"]
f[x_]:=Sqrt[x] Exp[-x] BesselI[0,x]
g[z_]:=f[1/z]
{err, approx}=MiniMaxApproximation[g[z],{z,{1/92.3,1/7.5},8,8},WorkingPrecision->70]
num=Numerator[approx][[1]];
den=Denominator[approx][[1]];
poly=num;
coeffs=CoefficientList[poly,z];
TableForm[Table[Row[{"'",NumberForm[coeffs[[i+1]],{50,50}, ExponentFunction->(Null&)],"',"}],{i,0,Length[coeffs]-1}]]