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<title>Debye Functions - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">7.10 Debye Functions</h3>
<p><a name="index-Debye-functions-420"></a>
The Debye functions D_n(x) are defined by the following integral,
<pre class="example"> D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1))
</pre>
<p class="noindent">For further information see Abramowitz &
Stegun, Section 27.1. The Debye functions are declared in the header
file <samp><span class="file">gsl_sf_debye.h</span></samp>.
<div class="defun">
— Function: double <b>gsl_sf_debye_1</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fdebye_005f1-421"></a></var><br>
— Function: int <b>gsl_sf_debye_1_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fdebye_005f1_005fe-422"></a></var><br>
<blockquote><p>These routines compute the first-order Debye function
D_1(x) = (1/x) \int_0^x dt (t/(e^t - 1)).
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_debye_2</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fdebye_005f2-423"></a></var><br>
— Function: int <b>gsl_sf_debye_2_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fdebye_005f2_005fe-424"></a></var><br>
<blockquote><p>These routines compute the second-order Debye function
D_2(x) = (2/x^2) \int_0^x dt (t^2/(e^t - 1)).
<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_debye_3</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fdebye_005f3-425"></a></var><br>
— Function: int <b>gsl_sf_debye_3_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fdebye_005f3_005fe-426"></a></var><br>
<blockquote><p>These routines compute the third-order Debye function
D_3(x) = (3/x^3) \int_0^x dt (t^3/(e^t - 1)).
<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_debye_4</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fdebye_005f4-427"></a></var><br>
— Function: int <b>gsl_sf_debye_4_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fdebye_005f4_005fe-428"></a></var><br>
<blockquote><p>These routines compute the fourth-order Debye function
D_4(x) = (4/x^4) \int_0^x dt (t^4/(e^t - 1)).
<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_debye_5</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fdebye_005f5-429"></a></var><br>
— Function: int <b>gsl_sf_debye_5_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fdebye_005f5_005fe-430"></a></var><br>
<blockquote><p>These routines compute the fifth-order Debye function
D_5(x) = (5/x^5) \int_0^x dt (t^5/(e^t - 1)).
<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_debye_6</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fdebye_005f6-431"></a></var><br>
— Function: int <b>gsl_sf_debye_6_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fdebye_005f6_005fe-432"></a></var><br>
<blockquote><p>These routines compute the sixth-order Debye function
D_6(x) = (6/x^6) \int_0^x dt (t^6/(e^t - 1)).
<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
</p></blockquote></div>
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