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DLMF:19.4#Ex1 - MaRDI portal

DLMF:19.4#Ex1 (Q6815)

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DLMF:19.4#Ex1
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    DLMF defining formula
    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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