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Statements
(
p
±
2
-
p
∓
2
)
R
J
(
x
2
,
y
2
,
z
2
,
p
2
)
=
2
(
p
±
2
-
a
2
)
R
J
(
a
2
,
z
+
2
,
z
-
2
,
p
±
2
)
-
3
R
F
(
x
2
,
y
2
,
z
2
)
+
3
R
C
(
z
2
,
p
2
)
,
superscript
subscript
𝑝
plus-or-minus
2
superscript
subscript
𝑝
minus-or-plus
2
Carlson-integral-RJ
superscript
𝑥
2
superscript
𝑦
2
superscript
𝑧
2
superscript
𝑝
2
2
superscript
subscript
𝑝
plus-or-minus
2
superscript
𝑎
2
Carlson-integral-RJ
superscript
𝑎
2
superscript
subscript
𝑧
2
superscript
subscript
𝑧
2
superscript
subscript
𝑝
plus-or-minus
2
3
Carlson-integral-RF
superscript
𝑥
2
superscript
𝑦
2
superscript
𝑧
2
3
Carlson-integral-RC
superscript
𝑧
2
superscript
𝑝
2
{\displaystyle{\displaystyle(p_{\pm}^{2}-p_{\mp}^{2})R_{J}\left(x^{2},y^{2},z^%
{2},p^{2}\right)=2(p_{\pm}^{2}-a^{2})R_{J}\left(a^{2},z_{+}^{2},z_{-}^{2},p_{%
\pm}^{2}\right)-3R_{F}\left(x^{2},y^{2},z^{2}\right)+3R_{C}\left(z^{2},p^{2}%
\right),}}
R
C
(
x
,
y
)
Carlson-integral-RC
𝑥
𝑦
{\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
R
F
(
x
,
y
,
z
)
Carlson-integral-RF
𝑥
𝑦
𝑧
{\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
R
J
(
x
,
y
,
z
,
p
)
Carlson-integral-RJ
𝑥
𝑦
𝑧
𝑝
{\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}%
\right)}}
