### 30.5 Derivatives and Integrals

The following functions allow a Chebyshev series to be differentiated or integrated, producing a new Chebyshev series. Note that the error estimate produced by evaluating the derivative series will be underestimated due to the contribution of higher order terms being neglected.

Function: int gsl_cheb_calc_deriv (gsl_cheb_series * deriv, const gsl_cheb_series * cs)

  This function computes the derivative of the series cs, storing the derivative coefficients in the previously allocated deriv. The two series cs and deriv must have been allocated with the same order.

Function: int gsl_cheb_calc_integ (gsl_cheb_series * integ, const gsl_cheb_series * cs)

  This function computes the integral of the series cs, storing the integral coefficients in the previously allocated integ. The two series cs and integ must have been allocated with the same order. The lower limit of the integration is taken to be the left hand end of the range a.