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<title>Legendre Form of Incomplete Elliptic Integrals - GNU Scientific Library -- Reference Manual</title>
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<h4 class="subsection">7.13.4 Legendre Form of Incomplete Elliptic Integrals</h4>
<div class="defun">
— Function: double <b>gsl_sf_ellint_F</b> (<var>double phi, double k, gsl_mode_t mode</var>)<var><a name="index-gsl_005fsf_005fellint_005fF-471"></a></var><br>
— Function: int <b>gsl_sf_ellint_F_e</b> (<var>double phi, double k, gsl_mode_t mode, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fellint_005fF_005fe-472"></a></var><br>
<blockquote><p>These routines compute the incomplete elliptic integral F(\phi,k)
to the accuracy specified by the mode variable <var>mode</var>.
Note that Abramowitz & Stegun define this function in terms of the
parameter m = k^2.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_ellint_E</b> (<var>double phi, double k, gsl_mode_t mode</var>)<var><a name="index-gsl_005fsf_005fellint_005fE-473"></a></var><br>
— Function: int <b>gsl_sf_ellint_E_e</b> (<var>double phi, double k, gsl_mode_t mode, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fellint_005fE_005fe-474"></a></var><br>
<blockquote><p>These routines compute the incomplete elliptic integral E(\phi,k)
to the accuracy specified by the mode variable <var>mode</var>.
Note that Abramowitz & Stegun define this function in terms of the
parameter m = k^2.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_ellint_P</b> (<var>double phi, double k, double n, gsl_mode_t mode</var>)<var><a name="index-gsl_005fsf_005fellint_005fP-475"></a></var><br>
— Function: int <b>gsl_sf_ellint_P_e</b> (<var>double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fellint_005fP_005fe-476"></a></var><br>
<blockquote><p>These routines compute the incomplete elliptic integral \Pi(\phi,k,n)
to the accuracy specified by the mode variable <var>mode</var>.
Note that Abramowitz & Stegun define this function in terms of the
parameters m = k^2 and \sin^2(\alpha) = k^2, with the
change of sign n \to -n.
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_ellint_D</b> (<var>double phi, double k, double n, gsl_mode_t mode</var>)<var><a name="index-gsl_005fsf_005fellint_005fD-477"></a></var><br>
— Function: int <b>gsl_sf_ellint_D_e</b> (<var>double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fellint_005fD_005fe-478"></a></var><br>
<blockquote><p>These functions compute the incomplete elliptic integral
D(\phi,k) which is defined through the Carlson form RD(x,y,z)
by the following relation,
The argument <var>n</var> is not used and will be removed in a future release.
<!-- Exceptional Return Values: GSL_EDOM -->
</blockquote></div>
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