Chebyshev Definitions - GNU Scientific Library -- Reference Manual
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Next: Creation and Calculation of Chebyshev Series, Up: Chebyshev Approximations

### 29.1 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.

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