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DLMF:19.24.E4
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Formula:7181
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MaRDI QID
Q7181
Label: DLMF:19.24.E4
Digital Library of Mathematical Functions ID
19.24.E4
2
p
(
2
y
z
+
y
p
+
z
p
)
-
1
/
2
≤
4
3
π
R
J
(
0
,
y
,
z
,
p
)
≤
(
y
z
p
2
)
-
3
/
8
.
2
𝑝
superscript
2
𝑦
𝑧
𝑦
𝑝
𝑧
𝑝
1
2
4
3
𝜋
Carlson-integral-RJ
0
𝑦
𝑧
𝑝
superscript
𝑦
𝑧
superscript
𝑝
2
3
8
{\displaystyle{\displaystyle\frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2}\leq\frac{4}{3% \pi}R_{J}\left(0,y,z,p\right)\leq(yzp^{2})^{-3/8}.}}
Constraint(s)
Symbols List
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)}}
: symmetric elliptic integral of third kind
π
{\displaystyle{\displaystyle\pi}}
: the ratio of the circumference of a circle to its diameter
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