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# 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`’.