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<title>Legendre Form of Complete Elliptic Integrals - GNU Scientific Library -- Reference Manual</title>
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<h4 class="subsection">7.13.3 Legendre Form of Complete Elliptic Integrals</h4>
<div class="defun">
— Function: double <b>gsl_sf_ellint_Kcomp</b> (<var>double k, gsl_mode_t mode</var>)<var><a name="index-gsl_005fsf_005fellint_005fKcomp-444"></a></var><br>
— Function: int <b>gsl_sf_ellint_Kcomp_e</b> (<var>double k, gsl_mode_t mode, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fellint_005fKcomp_005fe-445"></a></var><br>
<blockquote><p>These routines compute the complete elliptic integral K(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_Ecomp</b> (<var>double k, gsl_mode_t mode</var>)<var><a name="index-gsl_005fsf_005fellint_005fEcomp-446"></a></var><br>
— Function: int <b>gsl_sf_ellint_Ecomp_e</b> (<var>double k, gsl_mode_t mode, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fellint_005fEcomp_005fe-447"></a></var><br>
<blockquote><p>These routines compute the complete elliptic integral E(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_Pcomp</b> (<var>double k, double n, gsl_mode_t mode</var>)<var><a name="index-gsl_005fsf_005fellint_005fPcomp-448"></a></var><br>
— Function: int <b>gsl_sf_ellint_Pcomp_e</b> (<var>double k, double n, gsl_mode_t mode, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fellint_005fPcomp_005fe-449"></a></var><br>
<blockquote><p>These routines compute the complete elliptic integral \Pi(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>
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