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

[sf.cmath.sph.legendre]

29 Numerics library [numerics]

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

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.21 Spherical associated Legendre functions [sf.cmath.sph.legendre]

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floating-point-type sph_legendre(unsigned l, unsigned m, floating-point-type theta); float sph_legendref(unsigned l, unsigned m, float theta); long double sph_legendrel(unsigned l, unsigned m, long double theta);

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Effects: These functions compute the spherical associated Legendre functions of their respective argumentsl, m, and theta (theta measured in radians).

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Returns: Yℓm(θ,0), where Yℓm is given by Formula 29.41,l is l,m is m, andθ is theta.

Yℓm(θ,ϕ)=(−1)m[(2ℓ+1)4π(ℓ−m)!(ℓ+m)!]1/2Pℓm(cosθ)eimϕ , for |m|≤ℓ(29.41)

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

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See also [sf.cmath.assoc.legendre].