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DLMF:19.25#Ex5
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Formula:7201
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MaRDI QID
Q7201
Label: DLMF:19.25#Ex5
Digital Library of Mathematical Functions ID
19.25#Ex5
E
(
k
)
-
k
′
2
K
(
k
)
=
1
3
k
2
k
′
2
R
D
(
0
,
1
,
k
′
2
)
.
complete-elliptic-integral-second-kind-E
𝑘
superscript
superscript
𝑘
′
2
complete-elliptic-integral-first-kind-K
𝑘
1
3
superscript
𝑘
2
superscript
superscript
𝑘
′
2
Carlson-integral-RD
0
1
superscript
superscript
𝑘
′
2
{\displaystyle{\displaystyle E\left(k\right)-{k^{\prime}}^{2}K\left(k\right)=% \tfrac{1}{3}k^{2}{k^{\prime}}^{2}R_{D}\left(0,1,{k^{\prime}}^{2}\right).}}
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