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<title>Incomplete Fermi-Dirac Integrals - GNU Scientific Library -- Reference Manual</title>
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Previous: <a rel="previous" accesskey="p" href="Complete-Fermi_002dDirac-Integrals.html">Complete Fermi-Dirac Integrals</a>,
Up: <a rel="up" accesskey="u" href="Fermi_002dDirac-Function.html">Fermi-Dirac Function</a>
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<h4 class="subsection">7.18.2 Incomplete Fermi-Dirac Integrals</h4>
<p><a name="index-incomplete-Fermi_002dDirac-integral-555"></a><a name="index-Fj_0028x_002cb_0029_002c-incomplete-Fermi_002dDirac-integral-556"></a>The incomplete Fermi-Dirac integral F_j(x,b) is given by,
<pre class="example"> F_j(x,b) := (1/\Gamma(j+1)) \int_b^\infty dt (t^j / (\Exp(t-x) + 1))
</pre>
<div class="defun">
— Function: double <b>gsl_sf_fermi_dirac_inc_0</b> (<var>double x, double b</var>)<var><a name="index-gsl_005fsf_005ffermi_005fdirac_005finc_005f0-557"></a></var><br>
— Function: int <b>gsl_sf_fermi_dirac_inc_0_e</b> (<var>double x, double b, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005ffermi_005fdirac_005finc_005f0_005fe-558"></a></var><br>
<blockquote><p>These routines compute the incomplete Fermi-Dirac integral with an index
of zero,
<!-- {$F_0(x,b) = \ln(1 + e^{b-x}) - (b-x)$} -->
F_0(x,b) = \ln(1 + e^{b-x}) - (b-x).
<!-- Exceptional Return Values: GSL_EUNDRFLW, GSL_EDOM -->
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