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Previous: <a rel="previous" accesskey="p" href="Beta-Functions.html">Beta Functions</a>,
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<h4 class="subsection">7.19.6 Incomplete Beta Function</h4>
<div class="defun">
— Function: double <b>gsl_sf_beta_inc</b> (<var>double a, double b, double x</var>)<var><a name="index-gsl_005fsf_005fbeta_005finc-623"></a></var><br>
— Function: int <b>gsl_sf_beta_inc_e</b> (<var>double a, double b, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbeta_005finc_005fe-624"></a></var><br>
<blockquote><p><a name="index-incomplete-Beta-function_002c-normalized-625"></a><a name="index-normalized-incomplete-Beta-function-626"></a><a name="index-Beta-function_002c-incomplete-normalized-627"></a>These routines compute the normalized incomplete Beta function
I_x(a,b)=B_x(a,b)/B(a,b) where <!-- {$B_x(a,b) = \int_0^x t^{a-1} (1-t)^{b-1} dt$} -->
B_x(a,b) = \int_0^x t^{a-1} (1-t)^{b-1} dt
for <!-- {$0 \le x \le 1$} -->
0 <= x <= 1. For a > 0, b > 0 the value is computed using
a continued fraction expansion. For all other values it is computed using
the relation <!-- {$I_x(a,b,x) = (1/a) x^a {}_2F_1(a,1-b,a+1,x)/B(a,b)$} -->
I_x(a,b,x) = (1/a) x^a 2F1(a,1-b,a+1,x)/B(a,b).
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