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]}.