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<h3 class="section">7.25 Logarithm and Related Functions</h3>
<p><a name="index-logarithm-and-related-functions-726"></a>
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><span class="file">gsl_sf_log.h</span></samp>.
<div class="defun">
— Function: double <b>gsl_sf_log</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005flog-727"></a></var><br>
— Function: int <b>gsl_sf_log_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flog_005fe-728"></a></var><br>
<blockquote><p>These routines compute the logarithm of <var>x</var>, \log(x), for
x > 0.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_log_abs</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005flog_005fabs-729"></a></var><br>
— Function: int <b>gsl_sf_log_abs_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flog_005fabs_005fe-730"></a></var><br>
<blockquote><p>These routines compute the logarithm of the magnitude of <var>x</var>,
\log(|x|), for x \ne 0.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_sf_complex_log_e</b> (<var>double zr, double zi, gsl_sf_result * lnr, gsl_sf_result * theta</var>)<var><a name="index-gsl_005fsf_005fcomplex_005flog_005fe-731"></a></var><br>
<blockquote><p>This routine computes the complex logarithm of z = z_r + i
z_i. The results are returned as <var>lnr</var>, <var>theta</var> such that
\exp(lnr + i \theta) = z_r + i z_i, where \theta lies in
the range [-\pi,\pi].
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_log_1plusx</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005flog_005f1plusx-732"></a></var><br>
— Function: int <b>gsl_sf_log_1plusx_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flog_005f1plusx_005fe-733"></a></var><br>
<blockquote><p>These routines compute \log(1 + x) for x > -1 using an
algorithm that is accurate for small x.
<!-- Domain: x > -1.0 -->
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_log_1plusx_mx</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005flog_005f1plusx_005fmx-734"></a></var><br>
— Function: int <b>gsl_sf_log_1plusx_mx_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flog_005f1plusx_005fmx_005fe-735"></a></var><br>
<blockquote><p>These routines compute \log(1 + x) - x for x > -1 using an
algorithm that is accurate for small x.
<!-- Domain: x > -1.0 -->
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
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