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<title>Legendre Polynomials - GNU Scientific Library -- Reference Manual</title>
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<a name="Legendre-Polynomials"></a>
Next: <a rel="next" accesskey="n" href="Associated-Legendre-Polynomials-and-Spherical-Harmonics.html">Associated Legendre Polynomials and Spherical Harmonics</a>,
Up: <a rel="up" accesskey="u" href="Legendre-Functions-and-Spherical-Harmonics.html">Legendre Functions and Spherical Harmonics</a>
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<h4 class="subsection">7.24.1 Legendre Polynomials</h4>
<div class="defun">
— Function: double <b>gsl_sf_legendre_P1</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005flegendre_005fP1-682"></a></var><br>
— Function: double <b>gsl_sf_legendre_P2</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005flegendre_005fP2-683"></a></var><br>
— Function: double <b>gsl_sf_legendre_P3</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005flegendre_005fP3-684"></a></var><br>
— Function: int <b>gsl_sf_legendre_P1_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flegendre_005fP1_005fe-685"></a></var><br>
— Function: int <b>gsl_sf_legendre_P2_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flegendre_005fP2_005fe-686"></a></var><br>
— Function: int <b>gsl_sf_legendre_P3_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flegendre_005fP3_005fe-687"></a></var><br>
<blockquote><p>These functions evaluate the Legendre polynomials
<!-- {$P_l(x)$} -->
P_l(x) using explicit
representations for l=1, 2, 3.
<!-- Exceptional Return Values: none -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_legendre_Pl</b> (<var>int l, double x</var>)<var><a name="index-gsl_005fsf_005flegendre_005fPl-688"></a></var><br>
— Function: int <b>gsl_sf_legendre_Pl_e</b> (<var>int l, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flegendre_005fPl_005fe-689"></a></var><br>
<blockquote><p>These functions evaluate the Legendre polynomial <!-- {$P_l(x)$} -->
P_l(x) for a specific value of <var>l</var>,
<var>x</var> subject to <!-- {$l \ge 0$} -->
l >= 0,
<!-- {$|x| \le 1$} -->
|x| <= 1
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_sf_legendre_Pl_array</b> (<var>int lmax, double x, double result_array</var>[])<var><a name="index-gsl_005fsf_005flegendre_005fPl_005farray-690"></a></var><br>
— Function: int <b>gsl_sf_legendre_Pl_deriv_array</b> (<var>int lmax, double x, double result_array</var>[]<var>, double result_deriv_array</var>[])<var><a name="index-gsl_005fsf_005flegendre_005fPl_005fderiv_005farray-691"></a></var><br>
<blockquote>
<p>These functions compute an array of Legendre polynomials
P_l(x), and optionally their derivatives dP_l(x)/dx,
for l = 0, \dots, lmax,
<!-- {$|x| \le 1$} -->
|x| <= 1
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_legendre_Q0</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005flegendre_005fQ0-692"></a></var><br>
— Function: int <b>gsl_sf_legendre_Q0_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flegendre_005fQ0_005fe-693"></a></var><br>
<blockquote><p>These routines compute the Legendre function Q_0(x) for x >
-1, <!-- {$x \ne 1$} -->
x != 1.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_legendre_Q1</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005flegendre_005fQ1-694"></a></var><br>
— Function: int <b>gsl_sf_legendre_Q1_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flegendre_005fQ1_005fe-695"></a></var><br>
<blockquote><p>These routines compute the Legendre function Q_1(x) for x >
-1, <!-- {$x \ne 1$} -->
x != 1.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_legendre_Ql</b> (<var>int l, double x</var>)<var><a name="index-gsl_005fsf_005flegendre_005fQl-696"></a></var><br>
— Function: int <b>gsl_sf_legendre_Ql_e</b> (<var>int l, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flegendre_005fQl_005fe-697"></a></var><br>
<blockquote><p>These routines compute the Legendre function Q_l(x) for x >
-1, <!-- {$x \ne 1$} -->
x != 1 and <!-- {$l \ge 0$} -->
l >= 0.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
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