cppdraft_translate/cppdraft/sf/cmath/legendre.md

[sf.cmath.legendre]

29 Numerics library [numerics]

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

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.18 Legendre polynomials [sf.cmath.legendre]

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floating-point-type legendre(unsigned l, floating-point-type x); float legendref(unsigned l, float x); long double legendrel(unsigned l, long double x);

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Effects: These functions compute the Legendre polynomials of their respective argumentsl and x.

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

Pℓ(x)=12ℓℓ!dℓdxℓ(x2−1)ℓ , for |x|≤1(29.38)

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