alaguerre alegendre chebs chebt chebtd chebu gegenbauer gegenbauerd gegenbauerd1 hermite jacobi jacobid jacobid1 jacobid2 laguerre legendre legendred sharmonic sharmonic_sub sharmonici sharmonicr

alegendre() double alegendre ( unsigned int  n, unsigned int  m, double  x  ) Associated Legendre polynomial Pnm(x) Purpose alegendre computes the associated Legendre polynomial. Pnm(x) = (-1)^m (1 - x^2)^(m/2) dm/dxm Pn(x) Note that the term (-1)^m may not be included depending on the definition. Returns Associated Legendre polynomial Pnm(x). Parameters [in] n Degree of polynomial n. [in] m Order of polynomial m. [in] x Argument x (|x| <= 1). Error handling If |x| > 1, domain error (EDOM) occurs. Range error (ERANGE) may occur. Note Note that the worst errors occur when the degree increases, values greater than ~120 are very unlikely to produce sensible results, especially when the order is also large. Further the relative errors are likely to grow arbitrarily large when the function is very close to a root. Reference boost/math/special_functions