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<title>Digamma Function - GNU Scientific Library -- Reference Manual</title>
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<h4 class="subsection">7.28.1 Digamma Function</h4>
<div class="defun">
— Function: double <b>gsl_sf_psi_int</b> (<var>int n</var>)<var><a name="index-gsl_005fsf_005fpsi_005fint-763"></a></var><br>
— Function: int <b>gsl_sf_psi_int_e</b> (<var>int n, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fpsi_005fint_005fe-764"></a></var><br>
<blockquote><p>These routines compute the digamma function \psi(n) for positive
integer <var>n</var>. The digamma function is also called the Psi function.
<!-- Domain: n integer, n > 0 -->
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_psi</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fpsi-765"></a></var><br>
— Function: int <b>gsl_sf_psi_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fpsi_005fe-766"></a></var><br>
<blockquote><p>These routines compute the digamma function \psi(x) for general
x, x \ne 0.
<!-- Domain: x != 0.0, -1.0, -2.0, ... -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_ELOSS -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_psi_1piy</b> (<var>double y</var>)<var><a name="index-gsl_005fsf_005fpsi_005f1piy-767"></a></var><br>
— Function: int <b>gsl_sf_psi_1piy_e</b> (<var>double y, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fpsi_005f1piy_005fe-768"></a></var><br>
<blockquote><p>These routines compute the real part of the digamma function on the line
1+i y, \Re[\psi(1 + i y)].
<!-- exceptions: none -->
<!-- Exceptional Return Values: none -->
</p></blockquote></div>
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