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DLMF:19.4#Ex4 - MaRDI portal

DLMF:19.4#Ex4 (Q6818)

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DLMF:19.4#Ex4
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    DLMF defining formula
    d ( E ⁡ ( k ) - K ⁡ ( k ) ) d k = - k ⁢ E ⁡ ( k ) k ′ 2 , derivative complete-elliptic-integral-second-kind-E 𝑘 complete-elliptic-integral-first-kind-K 𝑘 𝑘 𝑘 complete-elliptic-integral-second-kind-E 𝑘 superscript superscript 𝑘 ′ 2 {\displaystyle{\displaystyle\frac{\mathrm{d}(E\left(k\right)-K\left(k\right))}% {\mathrm{d}k}=-\frac{kE\left(k\right)}{{k^{\prime}}^{2}},}}
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