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

chebu() double chebu ( unsigned int  n, double  x  ) Chebyshev polynomial of second kind Un(x) Purpose chebu computes the Chebyshev polynomial of the second kind Un(x). Un-1(x) = sin(nt)/sin(t), where x = cos(t) This polynomial follows the recurrence formula: Un+1(x) = 2xUn(x) - Un-1(x), where U0(x) = 1, U1(x) = 2x (n > 0) Returns Chebyshev polynomial of second kind Un(x). Parameters [in] n Argument n. [in] x Argument x. Error handling Range error (ERANGE) may occur. Note If x < -1 or x > 1, this routine is much slower and recommended not to be used. Reference boost/math/special_functions