cppdraft_translate/cppdraft/sf/cmath/cyl/bessel/i.md

[sf.cmath.cyl.bessel.i]

29 Numerics library [numerics]

29.7 Mathematical functions for floating-point types [c.math]

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.8 Regular modified cylindrical Bessel functions [sf.cmath.cyl.bessel.i]

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floating-point-type cyl_bessel_i(floating-point-type nu, floating-point-type x); float cyl_bessel_if(float nu, float x); long double cyl_bessel_il(long double nu, long double x);

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Effects: These functions compute the regular modified cylindrical Bessel functions of their respective argumentsnu and x.

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Returns: Iν(x), where Iν is given by Formula 29.28,ν is nu, andx is x.

Iν(x)=i−νJν(ix)=∞∑k=0(x/2)ν+2kk!Γ(ν+k+1) , for x≥0(29.28)

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Remarks: The effect of calling each of these functions is implementation-defined if nu >= 128.

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See also [sf.cmath.cyl.bessel.j].