— Function: gsl_cheb_series * gsl_cheb_alloc (const size_t n)

This function allocates space for a Chebyshev series of order n and returns a pointer to a new gsl_cheb_series struct.

— Function: void gsl_cheb_free (gsl_cheb_series * cs)

This function frees a previously allocated Chebyshev series cs.

— Function: int gsl_cheb_init (gsl_cheb_series * cs, const gsl_function * f, const double a, const double b)

This function computes the Chebyshev approximation cs for the function f over the range (a,b) to the previously specified order. The computation of the Chebyshev approximation is an O(n^2) process, and requires n function evaluations.