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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