# Chebyshev Approximations

This chapter describes routines for computing Chebyshev approximations to univariate functions. A Chebyshev approximation is a truncation of the series f(x) = \sum c_n T_n(x), where the Chebyshev polynomials T_n(x) = \cos(n \arccos x) provide an orthogonal basis of polynomials on the interval [-1,1] with the weight function 1 / \sqrt{1-x^2}. The first few Chebyshev polynomials are, T_0(x) = 1, T_1(x) = x, T_2(x) = 2 x^2 - 1.

The functions described in this chapter are declared in the header file ``gsl_chebyshev.h'`.

- The gsl_cheb_series struct
- Creation and Calculation of Chebyshev Series
- Chebyshev Series Evaluation
- Derivatives and Integrals
- Chebyshev Approximation examples
- Chebyshev Approximation References and Further Reading