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_series
The approximation is made over the range [a,b] using order+1 terms, including the coefficient c[0]. The series is computed using the following convention, which is needed when accessing the coefficients directly.