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Digital Library of Mathematical Functions ID
19.26.E18
R
F
(
x
,
y
,
z
)
=
2
R
F
(
x
+
λ
,
y
+
λ
,
z
+
λ
)
=
R
F
(
x
+
λ
4
,
y
+
λ
4
,
z
+
λ
4
)
,
Carlson-integral-RF
𝑥
𝑦
𝑧
2
Carlson-integral-RF
𝑥
𝜆
𝑦
𝜆
𝑧
𝜆
Carlson-integral-RF
𝑥
𝜆
4
𝑦
𝜆
4
𝑧
𝜆
4
{\displaystyle{\displaystyle R_{F}\left(x,y,z\right)=2R_{F}\left(x+\lambda,y+% \lambda,z+\lambda\right)=R_{F}\left(\frac{x+\lambda}{4},\frac{y+\lambda}{4},% \frac{z+\lambda}{4}\right),}}
Constraint(s)
Symbols List
R
F
(
x
,
y
,
z
)
Carlson-integral-RF
𝑥
𝑦
𝑧
{\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
: symmetric elliptic integral of first kind
λ
𝜆
{\displaystyle{\displaystyle\lambda}}
: positive
x
𝑥
{\displaystyle{\displaystyle x}}
: positive
y
𝑦
{\displaystyle{\displaystyle y}}
: positive
z
𝑧
{\displaystyle{\displaystyle z}}
: positive
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