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Next: <a href="Radial-Functions-for-Hyperbolic-Space.html#Radial-Functions-for-Hyperbolic-Space" accesskey="n" rel="next">Radial Functions for Hyperbolic Space</a>, Previous: <a href="Associated-Legendre-Polynomials-and-Spherical-Harmonics.html#Associated-Legendre-Polynomials-and-Spherical-Harmonics" accesskey="p" rel="previous">Associated Legendre Polynomials and Spherical Harmonics</a>, Up: <a href="Legendre-Functions-and-Spherical-Harmonics.html#Legendre-Functions-and-Spherical-Harmonics" accesskey="u" rel="up">Legendre Functions and Spherical Harmonics</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Conical-Functions-1"></a>
<h4 class="subsection">7.24.3 Conical Functions</h4>
<p>The Conical Functions <em>P^\mu_{-(1/2)+i\lambda}(x)</em> and <em>Q^\mu_{-(1/2)+i\lambda}</em>
are described in Abramowitz & Stegun, Section 8.12.
</p>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005fhalf"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_half</strong> <em>(double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005fhalf_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_half_e</strong> <em>(double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the irregular Spherical Conical Function
<em>P^{1/2}_{-1/2 + i \lambda}(x)</em> for <em>x > -1</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005fmhalf"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_mhalf</strong> <em>(double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005fmhalf_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_mhalf_e</strong> <em>(double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the regular Spherical Conical Function
<em>P^{-1/2}_{-1/2 + i \lambda}(x)</em> for <em>x > -1</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005f0"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_0</strong> <em>(double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005f0_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_0_e</strong> <em>(double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the conical function
<em>P^0_{-1/2 + i \lambda}(x)</em>
for <em>x > -1</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005f1"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_1</strong> <em>(double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005f1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_1_e</strong> <em>(double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the conical function
<em>P^1_{-1/2 + i \lambda}(x)</em> for <em>x > -1</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005fsph_005freg"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_sph_reg</strong> <em>(int <var>l</var>, double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005fsph_005freg_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_sph_reg_e</strong> <em>(int <var>l</var>, double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the Regular Spherical Conical Function
<em>P^{-1/2-l}_{-1/2 + i \lambda}(x)</em> for <em>x > -1</em>, <em>l >= -1</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005fcyl_005freg"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_cyl_reg</strong> <em>(int <var>m</var>, double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005fcyl_005freg_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_cyl_reg_e</strong> <em>(int <var>m</var>, double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the Regular Cylindrical Conical Function
<em>P^{-m}_{-1/2 + i \lambda}(x)</em> for <em>x > -1</em>, <em>m >= -1</em>.
</p></dd></dl>
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