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<title>GNU Scientific Library &ndash; Reference Manual: Pochhammer Symbol</title>

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<a name="Pochhammer-Symbol"></a>
<div class="header">
<p>
Next: <a href="Incomplete-Gamma-Functions.html#Incomplete-Gamma-Functions" accesskey="n" rel="next">Incomplete Gamma Functions</a>, Previous: <a href="Factorials.html#Factorials" accesskey="p" rel="previous">Factorials</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="Pochhammer-Symbol-1"></a>
<h4 class="subsection">7.19.3 Pochhammer Symbol</h4>

<dl>
<dt><a name="index-gsl_005fsf_005fpoch"></a>Function: <em>double</em> <strong>gsl_sf_poch</strong> <em>(double <var>a</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fpoch_005fe"></a>Function: <em>int</em> <strong>gsl_sf_poch_e</strong> <em>(double <var>a</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-Pochhammer-symbol"></a>
<a name="index-Apell-symbol_002c-see-Pochhammer-symbol"></a>
<p>These routines compute the Pochhammer symbol <em>(a)_x = \Gamma(a +
x)/\Gamma(a)</em>.  The Pochhammer symbol is also known as the Apell symbol and
sometimes written as <em>(a,x)</em>.  When <em>a</em> and <em>a+x</em> 
are negative integers or zero, the limiting value of the ratio is returned. 
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005flnpoch"></a>Function: <em>double</em> <strong>gsl_sf_lnpoch</strong> <em>(double <var>a</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flnpoch_005fe"></a>Function: <em>int</em> <strong>gsl_sf_lnpoch_e</strong> <em>(double <var>a</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-logarithm-of-Pochhammer-symbol"></a>
<p>These routines compute the logarithm of the Pochhammer symbol,
<em>\log((a)_x) = \log(\Gamma(a + x)/\Gamma(a))</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005flnpoch_005fsgn_005fe"></a>Function: <em>int</em> <strong>gsl_sf_lnpoch_sgn_e</strong> <em>(double <var>a</var>, double <var>x</var>, gsl_sf_result * <var>result</var>, double * <var>sgn</var>)</em></dt>
<dd><p>These routines compute the sign of the Pochhammer symbol and the
logarithm of its magnitude.  The computed parameters are <em>result =
\log(|(a)_x|)</em> with a corresponding error term,  
and <em>sgn = \sgn((a)_x)</em> where <em>(a)_x =
\Gamma(a + x)/\Gamma(a)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fpochrel"></a>Function: <em>double</em> <strong>gsl_sf_pochrel</strong> <em>(double <var>a</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fpochrel_005fe"></a>Function: <em>int</em> <strong>gsl_sf_pochrel_e</strong> <em>(double <var>a</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-relative-Pochhammer-symbol"></a>
<p>These routines compute the relative Pochhammer symbol <em>((a)_x -
1)/x</em> where <em>(a)_x = \Gamma(a + x)/\Gamma(a)</em>.
</p></dd></dl>





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