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<a name="Factorials"></a>
<div class="header">
<p>
Next: <a href="Pochhammer-Symbol.html#Pochhammer-Symbol" accesskey="n" rel="next">Pochhammer Symbol</a>, Previous: <a href="Gamma-Functions.html#Gamma-Functions" accesskey="p" rel="previous">Gamma Functions</a>, Up: <a href="Gamma-and-Beta-Functions.html#Gamma-and-Beta-Functions" accesskey="u" rel="up">Gamma and Beta Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Factorials-1"></a>
<h4 class="subsection">7.19.2 Factorials</h4>
<a name="index-factorial"></a>

<p>Although factorials can be computed from the Gamma function, using
the relation <em>n! = \Gamma(n+1)</em> for non-negative integer <em>n</em>,
it is usually more efficient to call the functions in this section,
particularly for small values of <em>n</em>, whose factorial values are
maintained in hardcoded tables.
</p>
<dl>
<dt><a name="index-gsl_005fsf_005ffact"></a>Function: <em>double</em> <strong>gsl_sf_fact</strong> <em>(unsigned int <var>n</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005ffact_005fe"></a>Function: <em>int</em> <strong>gsl_sf_fact_e</strong> <em>(unsigned int <var>n</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-factorial-1"></a>
<p>These routines compute the factorial <em>n!</em>.  The factorial is
related to the Gamma function by <em>n! = \Gamma(n+1)</em>.
The maximum value of <em>n</em> such that <em>n!</em> is not
considered an overflow is given by the macro <code>GSL_SF_FACT_NMAX</code>
and is 170.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fdoublefact"></a>Function: <em>double</em> <strong>gsl_sf_doublefact</strong> <em>(unsigned int <var>n</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdoublefact_005fe"></a>Function: <em>int</em> <strong>gsl_sf_doublefact_e</strong> <em>(unsigned int <var>n</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-double-factorial"></a>
<p>These routines compute the double factorial <em>n!! = n(n-2)(n-4) \dots</em>. 
The maximum value of <em>n</em> such that <em>n!!</em> is not
considered an overflow is given by the macro <code>GSL_SF_DOUBLEFACT_NMAX</code>
and is 297.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005flnfact"></a>Function: <em>double</em> <strong>gsl_sf_lnfact</strong> <em>(unsigned int <var>n</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flnfact_005fe"></a>Function: <em>int</em> <strong>gsl_sf_lnfact_e</strong> <em>(unsigned int <var>n</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-logarithm-of-factorial"></a>
<p>These routines compute the logarithm of the factorial of <var>n</var>,
<em>\log(n!)</em>.  The algorithm is faster than computing
<em>\ln(\Gamma(n+1))</em> via <code>gsl_sf_lngamma</code> for <em>n &lt; 170</em>,
but defers for larger <var>n</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005flndoublefact"></a>Function: <em>double</em> <strong>gsl_sf_lndoublefact</strong> <em>(unsigned int <var>n</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flndoublefact_005fe"></a>Function: <em>int</em> <strong>gsl_sf_lndoublefact_e</strong> <em>(unsigned int <var>n</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-logarithm-of-double-factorial"></a>
<p>These routines compute the logarithm of the double factorial of <var>n</var>,
<em>\log(n!!)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fchoose"></a>Function: <em>double</em> <strong>gsl_sf_choose</strong> <em>(unsigned int <var>n</var>, unsigned int <var>m</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fchoose_005fe"></a>Function: <em>int</em> <strong>gsl_sf_choose_e</strong> <em>(unsigned int <var>n</var>, unsigned int <var>m</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-combinatorial-factor-C_0028m_002cn_0029"></a>
<p>These routines compute the combinatorial factor <code>n choose m</code>
<em>= n!/(m!(n-m)!)</em>
</p></dd></dl>


<dl>
<dt><a name="index-gsl_005fsf_005flnchoose"></a>Function: <em>double</em> <strong>gsl_sf_lnchoose</strong> <em>(unsigned int <var>n</var>, unsigned int <var>m</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flnchoose_005fe"></a>Function: <em>int</em> <strong>gsl_sf_lnchoose_e</strong> <em>(unsigned int <var>n</var>, unsigned int <var>m</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-logarithm-of-combinatorial-factor-C_0028m_002cn_0029"></a>
<p>These routines compute the logarithm of <code>n choose m</code>.  This is
equivalent to the sum <em>\log(n!) - \log(m!) - \log((n-m)!)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005ftaylorcoeff"></a>Function: <em>double</em> <strong>gsl_sf_taylorcoeff</strong> <em>(int <var>n</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005ftaylorcoeff_005fe"></a>Function: <em>int</em> <strong>gsl_sf_taylorcoeff_e</strong> <em>(int <var>n</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-Taylor-coefficients_002c-computation-of"></a>
<p>These routines compute the Taylor coefficient <em>x^n / n!</em> for 
<em>x &gt;= 0</em>, 
<em>n &gt;= 0</em>.
</p></dd></dl>

<hr>
<div class="header">
<p>
Next: <a href="Pochhammer-Symbol.html#Pochhammer-Symbol" accesskey="n" rel="next">Pochhammer Symbol</a>, Previous: <a href="Gamma-Functions.html#Gamma-Functions" accesskey="p" rel="previous">Gamma Functions</a>, Up: <a href="Gamma-and-Beta-Functions.html#Gamma-and-Beta-Functions" accesskey="u" rel="up">Gamma and Beta Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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