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<title>GNU Scientific Library &ndash; Reference Manual: Legendre Polynomials</title>

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<a name="Legendre-Polynomials"></a>
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<p>
Next: <a href="Associated-Legendre-Polynomials-and-Spherical-Harmonics.html#Associated-Legendre-Polynomials-and-Spherical-Harmonics" accesskey="n" rel="next">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> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Legendre-Polynomials-1"></a>
<h4 class="subsection">7.24.1 Legendre Polynomials</h4>

<dl>
<dt><a name="index-gsl_005fsf_005flegendre_005fP1"></a>Function: <em>double</em> <strong>gsl_sf_legendre_P1</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flegendre_005fP2"></a>Function: <em>double</em> <strong>gsl_sf_legendre_P2</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flegendre_005fP3"></a>Function: <em>double</em> <strong>gsl_sf_legendre_P3</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flegendre_005fP1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_legendre_P1_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flegendre_005fP2_005fe"></a>Function: <em>int</em> <strong>gsl_sf_legendre_P2_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flegendre_005fP3_005fe"></a>Function: <em>int</em> <strong>gsl_sf_legendre_P3_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These functions evaluate the Legendre polynomials
<em>P_l(x)</em> using explicit
representations for <em>l=1, 2, 3</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005flegendre_005fPl"></a>Function: <em>double</em> <strong>gsl_sf_legendre_Pl</strong> <em>(int <var>l</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flegendre_005fPl_005fe"></a>Function: <em>int</em> <strong>gsl_sf_legendre_Pl_e</strong> <em>(int <var>l</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These functions evaluate the Legendre polynomial <em>P_l(x)</em> for a specific value of <var>l</var>,
<var>x</var> subject to <em>l &gt;= 0</em>, 
<em>|x| &lt;= 1</em>
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005flegendre_005fPl_005farray"></a>Function: <em>int</em> <strong>gsl_sf_legendre_Pl_array</strong> <em>(int <var>lmax</var>, double <var>x</var>, double <var>result_array</var>[])</em></dt>
<dt><a name="index-gsl_005fsf_005flegendre_005fPl_005fderiv_005farray"></a>Function: <em>int</em> <strong>gsl_sf_legendre_Pl_deriv_array</strong> <em>(int <var>lmax</var>, double <var>x</var>, double <var>result_array</var>[], double <var>result_deriv_array</var>[])</em></dt>
<dd>
<p>These functions compute arrays of Legendre polynomials
<em>P_l(x)</em> and derivatives <em>dP_l(x)/dx</em>, 
for <em>l = 0, \dots, lmax</em>, 
<em>|x| &lt;= 1</em>
</p></dd></dl>


<dl>
<dt><a name="index-gsl_005fsf_005flegendre_005fQ0"></a>Function: <em>double</em> <strong>gsl_sf_legendre_Q0</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flegendre_005fQ0_005fe"></a>Function: <em>int</em> <strong>gsl_sf_legendre_Q0_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the Legendre function <em>Q_0(x)</em> for <em>x &gt;
-1</em>, <em>x != 1</em>.
</p></dd></dl>


<dl>
<dt><a name="index-gsl_005fsf_005flegendre_005fQ1"></a>Function: <em>double</em> <strong>gsl_sf_legendre_Q1</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flegendre_005fQ1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_legendre_Q1_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the Legendre function <em>Q_1(x)</em> for <em>x &gt;
-1</em>, <em>x != 1</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005flegendre_005fQl"></a>Function: <em>double</em> <strong>gsl_sf_legendre_Ql</strong> <em>(int <var>l</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005flegendre_005fQl_005fe"></a>Function: <em>int</em> <strong>gsl_sf_legendre_Ql_e</strong> <em>(int <var>l</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the Legendre function <em>Q_l(x)</em> for <em>x &gt;
-1</em>, <em>x != 1</em> and <em>l &gt;= 0</em>.
</p></dd></dl>





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