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

legendre() double legendre ( unsigned int  n, double  x  ) Legendre polynomial Pn(x) Purpose legendre computes the Legendre polynomial. Pn(x) = 1/(2^n n!) dn/dxn(x^2 - 1)^n Returns Legendre polynomial Pn(x). Parameters [in] n Degree of polynomial n. [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. Further the relative errors are likely to grow arbitrarily large when the function is very close to a root. Reference boost/math/special_functions