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<title>Exponential Integral - GNU Scientific Library -- Reference Manual</title>
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<h4 class="subsection">7.17.1 Exponential Integral</h4>
<p><a name="index-E1_0028x_0029_002c-E2_0028x_0029_002c-Ei_0028x_0029-508"></a>
<div class="defun">
— Function: double <b>gsl_sf_expint_E1</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fexpint_005fE1-509"></a></var><br>
— Function: int <b>gsl_sf_expint_E1_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fexpint_005fE1_005fe-510"></a></var><br>
<blockquote><p>These routines compute the exponential integral E_1(x),
<pre class="example"> E_1(x) := \Re \int_1^\infty dt \exp(-xt)/t.
</pre>
<p class="noindent"><!-- Domain: x != 0.0 -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_expint_E2</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fexpint_005fE2-511"></a></var><br>
— Function: int <b>gsl_sf_expint_E2_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fexpint_005fE2_005fe-512"></a></var><br>
<blockquote><p>These routines compute the second-order exponential integral E_2(x),
<pre class="example"> E_2(x) := \Re \int_1^\infty dt \exp(-xt)/t^2.
</pre>
<p class="noindent"><!-- Domain: x != 0.0 -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_expint_En</b> (<var>int n, double x</var>)<var><a name="index-gsl_005fsf_005fexpint_005fEn-513"></a></var><br>
— Function: int <b>gsl_sf_expint_En_e</b> (<var>int n, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fexpint_005fEn_005fe-514"></a></var><br>
<blockquote><p>These routines compute the exponential integral E_n(x) of order n,
<pre class="example"> E_n(x) := \Re \int_1^\infty dt \exp(-xt)/t^n.
</pre>
<p class="noindent"><!-- Domain: x != 0.0 -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW -->
</p></blockquote></div>
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