DLMF:19.7.E8 (Q6203): Difference between revisions

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Property / constraint
 

α 2 ω 2 = k 2 superscript 𝛼 2 superscript 𝜔 2 superscript 𝑘 2 {\displaystyle{\displaystyle\alpha^{2}\omega^{2}=k^{2}}}

\alpha^{2}\omega^{2}=k^{2}
Property / constraint: α 2 ω 2 = k 2 superscript 𝛼 2 superscript 𝜔 2 superscript 𝑘 2 {\displaystyle{\displaystyle\alpha^{2}\omega^{2}=k^{2}}} / rank
 
Normal rank

Revision as of 18:05, 30 December 2019

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DLMF:19.7.E8
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    Statements

    Π ( ϕ , α 2 , k ) + Π ( ϕ , ω 2 , k ) = F ( ϕ , k ) + c R C ( ( c - 1 ) ( c - k 2 ) , ( c - α 2 ) ( c - ω 2 ) ) , elliptic-integral-third-kind-Pi italic-ϕ superscript 𝛼 2 𝑘 elliptic-integral-third-kind-Pi italic-ϕ superscript 𝜔 2 𝑘 elliptic-integral-first-kind-F italic-ϕ 𝑘 𝑐 Carlson-integral-RC 𝑐 1 𝑐 superscript 𝑘 2 𝑐 superscript 𝛼 2 𝑐 superscript 𝜔 2 {\displaystyle{\displaystyle\Pi\left(\phi,\alpha^{2},k\right)+\Pi\left(\phi,% \omega^{2},k\right)=F\left(\phi,k\right)+\sqrt{c}R_{C}\left((c-1)(c-k^{2}),(c-% \alpha^{2})(c-\omega^{2})\right),}}
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    DLMF:19.7.E8
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    α 2 ω 2 = k 2 superscript 𝛼 2 superscript 𝜔 2 superscript 𝑘 2 {\displaystyle{\displaystyle\alpha^{2}\omega^{2}=k^{2}}}
    0 references