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<title>Conical Functions - GNU Scientific Library -- Reference Manual</title>
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<a name="Conical-Functions"></a>
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<h4 class="subsection">7.24.3 Conical Functions</h4>
<p>The Conical Functions <!-- {$P^\mu_{-(1/2)+i\lambda}(x)$} -->
P^\mu_{-(1/2)+i\lambda}(x) and <!-- {$Q^\mu_{-(1/2)+i\lambda}$} -->
Q^\mu_{-(1/2)+i\lambda}
are described in Abramowitz & Stegun, Section 8.12.
<div class="defun">
— Function: double <b>gsl_sf_conicalP_half</b> (<var>double lambda, double x</var>)<var><a name="index-gsl_005fsf_005fconicalP_005fhalf-707"></a></var><br>
— Function: int <b>gsl_sf_conicalP_half_e</b> (<var>double lambda, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fconicalP_005fhalf_005fe-708"></a></var><br>
<blockquote><p>These routines compute the irregular Spherical Conical Function
<!-- {$P^{1/2}_{-1/2 + i \lambda}(x)$} -->
P^{1/2}_{-1/2 + i \lambda}(x) for x > -1.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_conicalP_mhalf</b> (<var>double lambda, double x</var>)<var><a name="index-gsl_005fsf_005fconicalP_005fmhalf-709"></a></var><br>
— Function: int <b>gsl_sf_conicalP_mhalf_e</b> (<var>double lambda, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fconicalP_005fmhalf_005fe-710"></a></var><br>
<blockquote><p>These routines compute the regular Spherical Conical Function
<!-- {$P^{-1/2}_{-1/2 + i \lambda}(x)$} -->
P^{-1/2}_{-1/2 + i \lambda}(x) for x > -1.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_conicalP_0</b> (<var>double lambda, double x</var>)<var><a name="index-gsl_005fsf_005fconicalP_005f0-711"></a></var><br>
— Function: int <b>gsl_sf_conicalP_0_e</b> (<var>double lambda, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fconicalP_005f0_005fe-712"></a></var><br>
<blockquote><p>These routines compute the conical function
<!-- {$P^0_{-1/2 + i \lambda}(x)$} -->
P^0_{-1/2 + i \lambda}(x)
for x > -1.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_conicalP_1</b> (<var>double lambda, double x</var>)<var><a name="index-gsl_005fsf_005fconicalP_005f1-713"></a></var><br>
— Function: int <b>gsl_sf_conicalP_1_e</b> (<var>double lambda, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fconicalP_005f1_005fe-714"></a></var><br>
<blockquote><p>These routines compute the conical function
<!-- {$P^1_{-1/2 + i \lambda}(x)$} -->
P^1_{-1/2 + i \lambda}(x) for x > -1.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_conicalP_sph_reg</b> (<var>int l, double lambda, double x</var>)<var><a name="index-gsl_005fsf_005fconicalP_005fsph_005freg-715"></a></var><br>
— Function: int <b>gsl_sf_conicalP_sph_reg_e</b> (<var>int l, double lambda, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fconicalP_005fsph_005freg_005fe-716"></a></var><br>
<blockquote><p>These routines compute the Regular Spherical Conical Function
<!-- {$P^{-1/2-l}_{-1/2 + i \lambda}(x)$} -->
P^{-1/2-l}_{-1/2 + i \lambda}(x) for x > -1, <!-- {$l \ge -1$} -->
l >= -1.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_conicalP_cyl_reg</b> (<var>int m, double lambda, double x</var>)<var><a name="index-gsl_005fsf_005fconicalP_005fcyl_005freg-717"></a></var><br>
— Function: int <b>gsl_sf_conicalP_cyl_reg_e</b> (<var>int m, double lambda, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fconicalP_005fcyl_005freg_005fe-718"></a></var><br>
<blockquote><p>These routines compute the Regular Cylindrical Conical Function
<!-- {$P^{-m}_{-1/2 + i \lambda}(x)$} -->
P^{-m}_{-1/2 + i \lambda}(x) for x > -1, <!-- {$m \ge -1$} -->
m >= -1.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
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