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<title>Definition of Carlson Forms - GNU Scientific Library -- Reference Manual</title>
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<h4 class="subsection">7.13.2 Definition of Carlson Forms</h4>
<p><a name="index-Carlson-forms-of-Elliptic-integrals-443"></a>The Carlson symmetric forms of elliptical integrals RC(x,y),
RD(x,y,z), RF(x,y,z) and RJ(x,y,z,p) are defined
by,
<pre class="example"> RC(x,y) = 1/2 \int_0^\infty dt (t+x)^(-1/2) (t+y)^(-1)
RD(x,y,z) = 3/2 \int_0^\infty dt (t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2)
RF(x,y,z) = 1/2 \int_0^\infty dt (t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2)
RJ(x,y,z,p) = 3/2 \int_0^\infty dt
(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1)
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