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<title>GNU Scientific Library – Reference Manual: Debye Functions</title>
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<a name="Debye-Functions"></a>
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<a name="Debye-Functions-1"></a>
<h3 class="section">7.10 Debye Functions</h3>
<a name="index-Debye-functions"></a>
<p>The Debye functions <em>D_n(x)</em> are defined by the following integral,
</p>
<div class="example">
<pre class="example">D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1))
</pre></div>
<p>For further information see Abramowitz &
Stegun, Section 27.1. The Debye functions are declared in the header
file <samp>gsl_sf_debye.h</samp>.
</p>
<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f1"></a>Function: <em>double</em> <strong>gsl_sf_debye_1</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_1_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the first-order Debye function
<em>D_1(x) = (1/x) \int_0^x dt (t/(e^t - 1))</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f2"></a>Function: <em>double</em> <strong>gsl_sf_debye_2</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f2_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_2_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the second-order Debye function
<em>D_2(x) = (2/x^2) \int_0^x dt (t^2/(e^t - 1))</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f3"></a>Function: <em>double</em> <strong>gsl_sf_debye_3</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f3_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_3_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the third-order Debye function
<em>D_3(x) = (3/x^3) \int_0^x dt (t^3/(e^t - 1))</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f4"></a>Function: <em>double</em> <strong>gsl_sf_debye_4</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f4_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_4_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the fourth-order Debye function
<em>D_4(x) = (4/x^4) \int_0^x dt (t^4/(e^t - 1))</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f5"></a>Function: <em>double</em> <strong>gsl_sf_debye_5</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f5_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_5_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the fifth-order Debye function
<em>D_5(x) = (5/x^5) \int_0^x dt (t^5/(e^t - 1))</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fdebye_005f6"></a>Function: <em>double</em> <strong>gsl_sf_debye_6</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fdebye_005f6_005fe"></a>Function: <em>int</em> <strong>gsl_sf_debye_6_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the sixth-order Debye function
<em>D_6(x) = (6/x^6) \int_0^x dt (t^6/(e^t - 1))</em>.
</p></dd></dl>
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