28 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. For further information see Abramowitz & Stegun, Chapter 22.

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

• Chebyshev Definitions
• Creation and Calculation of Chebyshev Series
• Chebyshev Series Evaluation
• Derivatives and Integrals
• Chebyshev Approximation examples
• Chebyshev Approximation References and Further Reading