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<h2 class="chapter">29 Chebyshev Approximations</h2>
<p><a name="index-Chebyshev-series-2292"></a><a name="index-fitting_002c-using-Chebyshev-polynomials-2293"></a><a name="index-interpolation_002c-using-Chebyshev-polynomials-2294"></a>
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 <!-- {$1 / \sqrt{1-x^2}$} -->
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.
<p>The functions described in this chapter are declared in the header file
<samp><span class="file">gsl_chebyshev.h</span></samp>.
<ul class="menu">
<li><a accesskey="1" href="Chebyshev-Definitions.html">Chebyshev Definitions</a>
<li><a accesskey="2" href="Creation-and-Calculation-of-Chebyshev-Series.html">Creation and Calculation of Chebyshev Series</a>
<li><a accesskey="3" href="Auxiliary-Functions-for-Chebyshev-Series.html">Auxiliary Functions for Chebyshev Series</a>
<li><a accesskey="4" href="Chebyshev-Series-Evaluation.html">Chebyshev Series Evaluation</a>
<li><a accesskey="5" href="Derivatives-and-Integrals.html">Derivatives and Integrals</a>
<li><a accesskey="6" href="Chebyshev-Approximation-Examples.html">Chebyshev Approximation Examples</a>
<li><a accesskey="7" href="Chebyshev-Approximation-References-and-Further-Reading.html">Chebyshev Approximation References and Further Reading</a>
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