Carlson symmetric form

In mathematics, the Carlson symmetric forms of elliptic integrals, RC(x,y), RD(x,y,z), RF(x,y,z) and RJ(x,y,z,p) are defined by

$RC(x,y) = \frac{1}{2} \int_0^\infty (t+x)^{-1/2} (t+y)^{-1}\,dt$

$RD(x,y,z) = \frac{3}{2} \int_0^\infty (t+x)^{-1/2} (t+y)^{-1/2} (t+z)^{-3/2}\,dt$

$RF(x,y,z) = \frac{1}{2} \int_0^\infty (t+x)^{-1/2} (t+y)^{-1/2} (t+z)^{-1/2}\,dt$

$RJ(x,y,z,p) = \frac{3}{2} \int_0^\infty (t+x)^{-1/2} (t+y)^{-1/2} (t+z)^{-1/2} (t+p)^{-1}\,dt$

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