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

[sf.cmath.cyl.bessel.k]

29 Numerics library [numerics]

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

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.10 Irregular modified cylindrical Bessel functions [sf.cmath.cyl.bessel.k]

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floating-point-type cyl_bessel_k(floating-point-type nu, floating-point-type x); float cyl_bessel_kf(float nu, float x); long double cyl_bessel_kl(long double nu, long double x);

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

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Returns: Kν(x), where Kν is given by Formula 29.30,ν is nu, andx is x.

Kν(x)=(π/2)iν+1(Jν(ix)+iNν(ix))=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩π2I−ν(x)−Iν(x)sinνπ,for x≥0 and non-integral νπ2limμ→νI−μ(x)−Iμ(x)sinμπ,for x≥0 and integral ν(29.30)

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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.i], [sf.cmath.cyl.bessel.j], [sf.cmath.cyl.neumann].