cppdraft_translate/cppdraft/sf/cmath/cyl/neumann.md

[sf.cmath.cyl.neumann]

29 Numerics library [numerics]

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

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.11 Cylindrical Neumann functions [sf.cmath.cyl.neumann]

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floating-point-type cyl_neumann(floating-point-type nu, floating-point-type x); float cyl_neumannf(float nu, float x); long double cyl_neumannl(long double nu, long double x);

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Effects: These functions compute the cylindrical Neumann functions, also known as the cylindrical Bessel functions of the second kind, of their respective argumentsnu and x.

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Returns: Nν(x), where Nν is given by Formula 29.31,ν is nu, andx is x.

Nν(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩Jν(x)cosνπ−J−ν(x)sinνπ,for x≥0 and non-integral νlimμ→νJμ(x)cosμπ−J−μ(x)sinμπ,for x≥0 and integral ν(29.31)

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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].