cppdraft_translate/cppdraft/sf/cmath/assoc/legendre.md

[sf.cmath.assoc.legendre]

29 Numerics library [numerics]

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

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.3 Associated Legendre functions [sf.cmath.assoc.legendre]

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floating-point-type assoc_legendre(unsigned l, unsigned m, floating-point-type x); float assoc_legendref(unsigned l, unsigned m, float x); long double assoc_legendrel(unsigned l, unsigned m, long double x);

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Effects: These functions compute the associated Legendre functions of their respective argumentsl, m, and x.

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Returns: Pℓm(x), where Pℓm is given by Formula 29.23,Pℓ is given by Formula 29.38,ℓ is l,m is m, andx is x.

Pℓm(x)=(1−x2)m/2dmdxmPℓ(x) , for |x|≤1(29.23)

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