### 30.1 Definitions

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,

    f(x) = (c_0 / 2) + \sum_{n=1} c_n T_n(x)

which is needed when accessing the coefficients directly.