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<a name="Chebyshev-Definitions"></a>
<div class="header">
<p>
Next: <a href="Creation-and-Calculation-of-Chebyshev-Series.html#Creation-and-Calculation-of-Chebyshev-Series" accesskey="n" rel="next">Creation and Calculation of Chebyshev Series</a>, Up: <a href="Chebyshev-Approximations.html#Chebyshev-Approximations" accesskey="u" rel="up">Chebyshev Approximations</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Definitions"></a>
<h3 class="section">30.1 Definitions</h3>
<a name="index-gsl_005fcheb_005fseries"></a>
<p>A Chebyshev series  is stored using the following structure,
</p>
<div class="example">
<pre class="example">typedef struct
{
  double * c;   /* coefficients  c[0] .. c[order] */
  int order;    /* order of expansion             */
  double a;     /* lower interval point           */
  double b;     /* upper interval point           */
  ...
} gsl_cheb_series
</pre></div>

<p>The approximation is made over the range <em>[a,b]</em> using
<var>order</var>+1 terms, including the coefficient <em>c[0]</em>.  The series
is computed using the following convention,
</p>
<div class="example">
<pre class="example">f(x) = (c_0 / 2) + \sum_{n=1} c_n T_n(x)
</pre></div>

<p>which is needed when accessing the coefficients directly.
</p>



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