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Next: <a rel="next" accesskey="n" href="Riemann-Zeta-Function-Minus-One.html">Riemann Zeta Function Minus One</a>,
Up: <a rel="up" accesskey="u" href="Zeta-Functions.html">Zeta Functions</a>
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<h4 class="subsection">7.32.1 Riemann Zeta Function</h4>
<p><a name="index-Riemann-Zeta-Function-850"></a>
The Riemann zeta function is defined by the infinite sum
<!-- {$\zeta(s) = \sum_{k=1}^\infty k^{-s}$} -->
\zeta(s) = \sum_{k=1}^\infty k^{-s}.
<div class="defun">
— Function: double <b>gsl_sf_zeta_int</b> (<var>int n</var>)<var><a name="index-gsl_005fsf_005fzeta_005fint-851"></a></var><br>
— Function: int <b>gsl_sf_zeta_int_e</b> (<var>int n, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fzeta_005fint_005fe-852"></a></var><br>
<blockquote><p>These routines compute the Riemann zeta function \zeta(n)
for integer <var>n</var>,
n \ne 1.
<!-- Domain: n integer, n != 1 -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_zeta</b> (<var>double s</var>)<var><a name="index-gsl_005fsf_005fzeta-853"></a></var><br>
— Function: int <b>gsl_sf_zeta_e</b> (<var>double s, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fzeta_005fe-854"></a></var><br>
<blockquote><p>These routines compute the Riemann zeta function \zeta(s)
for arbitrary <var>s</var>,
s \ne 1.
<!-- Domain: s != 1.0 -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW -->
</p></blockquote></div>
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