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<title>GNU Scientific Library &ndash; Reference Manual: Real Argument</title>

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Next: <a href="Complex-Argument.html#Complex-Argument" accesskey="n" rel="next">Complex Argument</a>, Up: <a href="Dilogarithm.html#Dilogarithm" accesskey="u" rel="up">Dilogarithm</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Real-Argument-1"></a>
<h4 class="subsection">7.11.1 Real Argument</h4>

<dl>
<dt><a name="index-gsl_005fsf_005fdilog"></a>Function: <em>double</em> <strong>gsl_sf_dilog</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdilog_005fe"></a>Function: <em>int</em> <strong>gsl_sf_dilog_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the dilogarithm for a real argument. In Lewin&rsquo;s
notation this is <em>Li_2(x)</em>, the real part of the dilogarithm of a
real <em>x</em>.  It is defined by the integral representation
<em>Li_2(x) = - \Re \int_0^x ds \log(1-s) / s</em>.  
Note that <em>\Im(Li_2(x)) = 0</em> for <em>x &lt;= 1</em>, and <em>-\pi\log(x)</em> for <em>x &gt; 1</em>.
</p>
<p>Note that Abramowitz &amp; Stegun refer to the Spence integral
<em>S(x)=Li_2(1-x)</em> as the dilogarithm rather than <em>Li_2(x)</em>.
</p></dd></dl>




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