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<title>Incomplete Gamma Functions - GNU Scientific Library -- Reference Manual</title>
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<a name="Incomplete-Gamma-Functions"></a>
Next: <a rel="next" accesskey="n" href="Beta-Functions.html">Beta Functions</a>,
Previous: <a rel="previous" accesskey="p" href="Pochhammer-Symbol.html">Pochhammer Symbol</a>,
Up: <a rel="up" accesskey="u" href="Gamma-and-Beta-Functions.html">Gamma and Beta Functions</a>
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<h4 class="subsection">7.19.4 Incomplete Gamma Functions</h4>
<div class="defun">
— Function: double <b>gsl_sf_gamma_inc</b> (<var>double a, double x</var>)<var><a name="index-gsl_005fsf_005fgamma_005finc-607"></a></var><br>
— Function: int <b>gsl_sf_gamma_inc_e</b> (<var>double a, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fgamma_005finc_005fe-608"></a></var><br>
<blockquote><p><a name="index-non_002dnormalized-incomplete-Gamma-function-609"></a><a name="index-unnormalized-incomplete-Gamma-function-610"></a>These functions compute the unnormalized incomplete Gamma Function
<!-- {$\Gamma(a,x) = \int_x^\infty dt\, t^{(a-1)} \exp(-t)$} -->
\Gamma(a,x) = \int_x^\infty dt t^{a-1} \exp(-t)
for a real and <!-- {$x \ge 0$} -->
x >= 0.
<!-- exceptions: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_gamma_inc_Q</b> (<var>double a, double x</var>)<var><a name="index-gsl_005fsf_005fgamma_005finc_005fQ-611"></a></var><br>
— Function: int <b>gsl_sf_gamma_inc_Q_e</b> (<var>double a, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fgamma_005finc_005fQ_005fe-612"></a></var><br>
<blockquote><p><a name="index-incomplete-Gamma-function-613"></a>These routines compute the normalized incomplete Gamma Function
<!-- {$Q(a,x) = 1/\Gamma(a) \int_x^\infty dt\, t^{(a-1)} \exp(-t)$} -->
Q(a,x) = 1/\Gamma(a) \int_x^\infty dt t^{a-1} \exp(-t)
for a > 0, <!-- {$x \ge 0$} -->
x >= 0.
<!-- exceptions: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_gamma_inc_P</b> (<var>double a, double x</var>)<var><a name="index-gsl_005fsf_005fgamma_005finc_005fP-614"></a></var><br>
— Function: int <b>gsl_sf_gamma_inc_P_e</b> (<var>double a, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fgamma_005finc_005fP_005fe-615"></a></var><br>
<blockquote><p><a name="index-complementary-incomplete-Gamma-function-616"></a>These routines compute the complementary normalized incomplete Gamma Function
<!-- {$P(a,x) = 1 - Q(a,x) = 1/\Gamma(a) \int_0^x dt\, t^{(a-1)} \exp(-t)$} -->
P(a,x) = 1 - Q(a,x) = 1/\Gamma(a) \int_0^x dt t^{a-1} \exp(-t)
for a > 0, <!-- {$x \ge 0$} -->
x >= 0.
<p>Note that Abramowitz & Stegun call P(a,x) the incomplete gamma
function (section 6.5).
<!-- exceptions: GSL_EDOM -->
</p></blockquote></div>
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