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<title>GNU Scientific Library – Reference Manual: Incomplete Beta Function</title>
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Previous: <a href="Beta-Functions.html#Beta-Functions" accesskey="p" rel="previous">Beta Functions</a>, Up: <a href="Gamma-and-Beta-Functions.html#Gamma-and-Beta-Functions" accesskey="u" rel="up">Gamma and Beta Functions</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Incomplete-Beta-Function-1"></a>
<h4 class="subsection">7.19.6 Incomplete Beta Function</h4>
<dl>
<dt><a name="index-gsl_005fsf_005fbeta_005finc"></a>Function: <em>double</em> <strong>gsl_sf_beta_inc</strong> <em>(double <var>a</var>, double <var>b</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbeta_005finc_005fe"></a>Function: <em>int</em> <strong>gsl_sf_beta_inc_e</strong> <em>(double <var>a</var>, double <var>b</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><a name="index-incomplete-Beta-function_002c-normalized"></a>
<a name="index-normalized-incomplete-Beta-function"></a>
<a name="index-Beta-function_002c-incomplete-normalized"></a>
<p>These routines compute the normalized incomplete Beta function
<em>I_x(a,b)=B_x(a,b)/B(a,b)</em> where <em>B_x(a,b) = \int_0^x t^{a-1} (1-t)^{b-1} dt</em>
for <em>0 <= x <= 1</em>. For <em>a > 0</em>, <em>b > 0</em> the value is computed using
a continued fraction expansion. For all other values it is computed using
the relation <em>I_x(a,b,x) = (1/a) x^a 2F1(a,1-b,a+1,x)/B(a,b)</em>.
</p></dd></dl>
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