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DLMF:19.4#Ex1
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Formula:6815
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MaRDI QID
Q6815
Label: DLMF:19.4#Ex1
Digital Library of Mathematical Functions ID
19.4#Ex1
d
K
(
k
)
d
k
=
E
(
k
)
-
k
′
2
K
(
k
)
k
k
′
2
,
derivative
complete-elliptic-integral-first-kind-K
𝑘
𝑘
complete-elliptic-integral-second-kind-E
𝑘
superscript
superscript
𝑘
′
2
complete-elliptic-integral-first-kind-K
𝑘
𝑘
superscript
superscript
𝑘
′
2
{\displaystyle{\displaystyle\frac{\mathrm{d}K\left(k\right)}{\mathrm{d}k}=% \frac{E\left(k\right)-{k^{\prime}}^{2}K\left(k\right)}{k{k^{\prime}}^{2}},}}
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