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<title>GNU Scientific Library &ndash; Reference Manual: Eta Function</title>

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<a name="Eta-Function"></a>
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<p>
Previous: <a href="Hurwitz-Zeta-Function.html#Hurwitz-Zeta-Function" accesskey="p" rel="previous">Hurwitz Zeta Function</a>, Up: <a href="Zeta-Functions.html#Zeta-Functions" accesskey="u" rel="up">Zeta Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Eta-Function-1"></a>
<h4 class="subsection">7.32.4 Eta Function</h4>
<a name="index-Eta-Function"></a>

<p>The eta function is defined by
<em>\eta(s) = (1-2^{1-s}) \zeta(s)</em>.
</p>
<dl>
<dt><a name="index-gsl_005fsf_005feta_005fint"></a>Function: <em>double</em> <strong>gsl_sf_eta_int</strong> <em>(int <var>n</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005feta_005fint_005fe"></a>Function: <em>int</em> <strong>gsl_sf_eta_int_e</strong> <em>(int <var>n</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the eta function <em>\eta(n)</em> for integer <var>n</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005feta"></a>Function: <em>double</em> <strong>gsl_sf_eta</strong> <em>(double <var>s</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005feta_005fe"></a>Function: <em>int</em> <strong>gsl_sf_eta_e</strong> <em>(double <var>s</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the eta function <em>\eta(s)</em> for arbitrary <var>s</var>.
</p></dd></dl>





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