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<title>GNU Scientific Library – Reference Manual: Logarithm and Related Functions</title>
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<a name="Logarithm-and-Related-Functions"></a>
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Next: <a href="Mathieu-Functions.html#Mathieu-Functions" accesskey="n" rel="next">Mathieu Functions</a>, Previous: <a href="Legendre-Functions-and-Spherical-Harmonics.html#Legendre-Functions-and-Spherical-Harmonics" accesskey="p" rel="previous">Legendre Functions and Spherical Harmonics</a>, Up: <a href="Special-Functions.html#Special-Functions" accesskey="u" rel="up">Special Functions</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Logarithm-and-Related-Functions-1"></a>
<h3 class="section">7.25 Logarithm and Related Functions</h3>
<a name="index-logarithm-and-related-functions"></a>
<p>Information on the properties of the Logarithm function can be found in
Abramowitz & Stegun, Chapter 4. The functions described in this section
are declared in the header file <samp>gsl_sf_log.h</samp>.
</p>
<dl>
<dt><a name="index-gsl_005fsf_005flog"></a>Function: <em>double</em> <strong>gsl_sf_log</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flog_005fe"></a>Function: <em>int</em> <strong>gsl_sf_log_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the logarithm of <var>x</var>, <em>\log(x)</em>, for
<em>x > 0</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005flog_005fabs"></a>Function: <em>double</em> <strong>gsl_sf_log_abs</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flog_005fabs_005fe"></a>Function: <em>int</em> <strong>gsl_sf_log_abs_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the logarithm of the magnitude of <var>x</var>,
<em>\log(|x|)</em>, for <em>x \ne 0</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fcomplex_005flog_005fe"></a>Function: <em>int</em> <strong>gsl_sf_complex_log_e</strong> <em>(double <var>zr</var>, double <var>zi</var>, gsl_sf_result * <var>lnr</var>, gsl_sf_result * <var>theta</var>)</em></dt>
<dd><p>This routine computes the complex logarithm of <em>z = z_r + i
z_i</em>. The results are returned as <var>lnr</var>, <var>theta</var> such that
<em>\exp(lnr + i \theta) = z_r + i z_i</em>, where <em>\theta</em> lies in
the range <em>[-\pi,\pi]</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005flog_005f1plusx"></a>Function: <em>double</em> <strong>gsl_sf_log_1plusx</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flog_005f1plusx_005fe"></a>Function: <em>int</em> <strong>gsl_sf_log_1plusx_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute <em>\log(1 + x)</em> for <em>x > -1</em> using an
algorithm that is accurate for small <em>x</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005flog_005f1plusx_005fmx"></a>Function: <em>double</em> <strong>gsl_sf_log_1plusx_mx</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flog_005f1plusx_005fmx_005fe"></a>Function: <em>int</em> <strong>gsl_sf_log_1plusx_mx_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute <em>\log(1 + x) - x</em> for <em>x > -1</em> using an
algorithm that is accurate for small <em>x</em>.
</p></dd></dl>
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