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<a name="Legendre-Form-of-Incomplete-Elliptic-Integrals"></a>
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Next: <a href="Carlson-Forms.html#Carlson-Forms" accesskey="n" rel="next">Carlson Forms</a>, Previous: <a href="Legendre-Form-of-Complete-Elliptic-Integrals.html#Legendre-Form-of-Complete-Elliptic-Integrals" accesskey="p" rel="previous">Legendre Form of Complete Elliptic Integrals</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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<hr>
<a name="Legendre-Form-of-Incomplete-Elliptic-Integrals-1"></a>
<h4 class="subsection">7.13.4 Legendre Form of Incomplete Elliptic Integrals</h4>

<dl>
<dt><a name="index-gsl_005fsf_005fellint_005fF"></a>Function: <em>double</em> <strong>gsl_sf_ellint_F</strong> <em>(double <var>phi</var>, double <var>k</var>, gsl_mode_t <var>mode</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fellint_005fF_005fe"></a>Function: <em>int</em> <strong>gsl_sf_ellint_F_e</strong> <em>(double <var>phi</var>, double <var>k</var>, gsl_mode_t <var>mode</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the incomplete elliptic integral <em>F(\phi,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_005fE"></a>Function: <em>double</em> <strong>gsl_sf_ellint_E</strong> <em>(double <var>phi</var>, double <var>k</var>, gsl_mode_t <var>mode</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fellint_005fE_005fe"></a>Function: <em>int</em> <strong>gsl_sf_ellint_E_e</strong> <em>(double <var>phi</var>, double <var>k</var>, gsl_mode_t <var>mode</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the incomplete elliptic integral <em>E(\phi,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_005fP"></a>Function: <em>double</em> <strong>gsl_sf_ellint_P</strong> <em>(double <var>phi</var>, double <var>k</var>, double <var>n</var>, gsl_mode_t <var>mode</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fellint_005fP_005fe"></a>Function: <em>int</em> <strong>gsl_sf_ellint_P_e</strong> <em>(double <var>phi</var>, 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 incomplete elliptic integral <em>\Pi(\phi,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>

<dl>
<dt><a name="index-gsl_005fsf_005fellint_005fD"></a>Function: <em>double</em> <strong>gsl_sf_ellint_D</strong> <em>(double <var>phi</var>, double <var>k</var>, gsl_mode_t <var>mode</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fellint_005fD_005fe"></a>Function: <em>int</em> <strong>gsl_sf_ellint_D_e</strong> <em>(double <var>phi</var>, double <var>k</var>, gsl_mode_t <var>mode</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These functions compute the incomplete elliptic integral
<em>D(\phi,k)</em> which is defined through the Carlson form <em>RD(x,y,z)</em>
by the following relation, 
</p>
<div class="example">
<pre class="example">D(\phi,k) = (1/3)(\sin(\phi))^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).
</pre></div>

</dd></dl>





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