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Next: <a href="Legendre-Form-of-Incomplete-Elliptic-Integrals.html#Legendre-Form-of-Incomplete-Elliptic-Integrals" accesskey="n" rel="next">Legendre Form of Incomplete Elliptic Integrals</a>, Previous: <a href="Definition-of-Carlson-Forms.html#Definition-of-Carlson-Forms" accesskey="p" rel="previous">Definition of Carlson Forms</a>, Up: <a href="Elliptic-Integrals.html#Elliptic-Integrals" accesskey="u" rel="up">Elliptic Integrals</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Legendre-Form-of-Complete-Elliptic-Integrals-1"></a>
<h4 class="subsection">7.13.3 Legendre Form of Complete Elliptic Integrals</h4>

<dl>
<dt><a name="index-gsl_005fsf_005fellint_005fKcomp"></a>Function: <em>double</em> <strong>gsl_sf_ellint_Kcomp</strong> <em>(double <var>k</var>, gsl_mode_t <var>mode</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fellint_005fKcomp_005fe"></a>Function: <em>int</em> <strong>gsl_sf_ellint_Kcomp_e</strong> <em>(double <var>k</var>, gsl_mode_t <var>mode</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the complete elliptic integral <em>K(k)</em> to
the accuracy specified by the mode variable <var>mode</var>.  
Note that Abramowitz &amp; Stegun define this function in terms of the
parameter <em>m = k^2</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fellint_005fEcomp"></a>Function: <em>double</em> <strong>gsl_sf_ellint_Ecomp</strong> <em>(double <var>k</var>, gsl_mode_t <var>mode</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fellint_005fEcomp_005fe"></a>Function: <em>int</em> <strong>gsl_sf_ellint_Ecomp_e</strong> <em>(double <var>k</var>, gsl_mode_t <var>mode</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the complete elliptic integral <em>E(k)</em> to the
accuracy specified by the mode variable <var>mode</var>.
Note that Abramowitz &amp; Stegun define this function in terms of the
parameter <em>m = k^2</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fellint_005fPcomp"></a>Function: <em>double</em> <strong>gsl_sf_ellint_Pcomp</strong> <em>(double <var>k</var>, double <var>n</var>, gsl_mode_t <var>mode</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fellint_005fPcomp_005fe"></a>Function: <em>int</em> <strong>gsl_sf_ellint_Pcomp_e</strong> <em>(double <var>k</var>, double <var>n</var>,  gsl_mode_t <var>mode</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the complete elliptic integral <em>\Pi(k,n)</em> to the
accuracy specified by the mode variable <var>mode</var>.
Note that Abramowitz &amp; Stegun define this function in terms of the
parameters <em>m = k^2</em> and <em>\sin^2(\alpha) = k^2</em>, with the
change of sign <em>n \to -n</em>.
</p></dd></dl>




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