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k0_small_dd

pxfm::bessel::k0

Function k0_small_dd 

Source 
pub(crate) fn k0_small_dd(x: f64) -> DoubleDouble
Expand description

K0(x) + log(x) * I0(x) = P(x^2) hence K0(x) = P(x^2) - log(x)*I0(x)

Generated in Wolfram Mathematica:

<<FunctionApproximations`
ClearAll["Global`*"]
f[x_]:=BesselK[0,x]+Log[x]BesselI[0,x]
g[z_]:=f[Sqrt[z]]
{err,approx}=MiniMaxApproximation[g[z],{z,{0.000000001,1},5,5},WorkingPrecision->60]
poly=Numerator[approx][[1]];
coeffs=CoefficientList[poly,z];
TableForm[Table[Row[{"'",NumberForm[coeffs[[i+1]],{50,50},ExponentFunction->(Null&)],"',"}],{i,0,Length[coeffs]-1}]]
poly=Denominator[approx][[1]];
coeffs=CoefficientList[poly,z];
TableForm[Table[Row[{"'",NumberForm[coeffs[[i+1]],{50,50},ExponentFunction->(Null&)],"',"}],{i,0,Length[coeffs]-1}]]