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

[sf.cmath.assoc.laguerre]

29 Numerics library [numerics]

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

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.2 Associated Laguerre polynomials [sf.cmath.assoc.laguerre]

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floating-point-type assoc_laguerre(unsigned n, unsigned m, floating-point-type x); float assoc_laguerref(unsigned n, unsigned m, float x); long double assoc_laguerrel(unsigned n, unsigned m, long double x);

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Effects: These functions compute the associated Laguerre polynomials of their respective argumentsn, m, and x.

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Returns: Lmn(x), where Lmn is given by Formula 29.22,Ln+m is given by Formula 29.37,n is n,m is m, andx is x.

Lmn(x)=(−1)mdmdxmLn+m(x) , for x≥0(29.22)

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