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DLMF:19.8#Ex11
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Formula:6920
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MaRDI QID
Q6920
Label: DLMF:19.8#Ex11
Digital Library of Mathematical Functions ID
19.8#Ex11
E
(
ϕ
,
k
)
=
1
2
(
1
+
k
′
)
E
(
ϕ
1
,
k
1
)
-
k
′
F
(
ϕ
,
k
)
+
1
2
(
1
-
k
′
)
sin
ϕ
1
.
elliptic-integral-second-kind-E
italic-ϕ
𝑘
1
2
1
superscript
𝑘
′
elliptic-integral-second-kind-E
subscript
italic-ϕ
1
subscript
𝑘
1
superscript
𝑘
′
elliptic-integral-first-kind-F
italic-ϕ
𝑘
1
2
1
superscript
𝑘
′
subscript
italic-ϕ
1
{\displaystyle{\displaystyle E\left(\phi,k\right)=\tfrac{1}{2}(1+k^{\prime})E% \left(\phi_{1},k_{1}\right)-k^{\prime}F\left(\phi,k\right)+\tfrac{1}{2}(1-k^{% \prime})\sin\phi_{1}.}}
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