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i0ef_1_to_3p5

pxfm::bessel::i0ef

Function i0ef_1_to_3p5 

Source 
fn i0ef_1_to_3p5(x: f32, v_exp: f64) -> f32
Expand description

Computes I0.

/// Valid only on interval [1;3.5]

as rational approximation I0 = 1 + (x/2)^2 * Pn((x/2)^2)/Qm((x/2)^2))

Generated by Wolram Mathematica:

<<FunctionApproximations`
ClearAll["Global`*"]
f[x_]:=(BesselI[0,x]-1)/(x/2)^2
g[z_]:=f[2 Sqrt[z]]
{err, approx}=MiniMaxApproximation[g[z],{z,{1,3.5},5,4},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}]]