A Chebyshev series is stored using the following structure,
typedef struct
{
double * c; /* coefficients c[0] .. c[order] */
int order; /* order of expansion */
double a; /* lower interval point */
double b; /* upper interval point */
} gsl_cheb_struct
The approximation is made over the range @math{[a,b]} using order+1 terms, including the coefficient @math{c[0]}.