DLMF:19.7.E10 (Q6205): Difference between revisions

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Property / constraint
 

( k 2 - α 2 ) ( k 2 - ω 2 ) = k 2 ( k 2 - 1 ) superscript 𝑘 2 superscript 𝛼 2 superscript 𝑘 2 superscript 𝜔 2 superscript 𝑘 2 superscript 𝑘 2 1 {\displaystyle{\displaystyle(k^{2}-\alpha^{2})(k^{2}-\omega^{2})=k^{2}(k^{2}-1% )}}

(k^{2}-\alpha^{2})(k^{2}-\omega^{2})=k^{2}(k^{2}-1)
Property / constraint: ( k 2 - α 2 ) ( k 2 - ω 2 ) = k 2 ( k 2 - 1 ) superscript 𝑘 2 superscript 𝛼 2 superscript 𝑘 2 superscript 𝜔 2 superscript 𝑘 2 superscript 𝑘 2 1 {\displaystyle{\displaystyle(k^{2}-\alpha^{2})(k^{2}-\omega^{2})=k^{2}(k^{2}-1% )}} / rank
 
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Revision as of 18:05, 30 December 2019

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DLMF:19.7.E10
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    Statements

    ( 1 - α 2 ) Π ( ϕ , α 2 , k ) + ( 1 - ω 2 ) Π ( ϕ , ω 2 , k ) = F ( ϕ , k ) + ( 1 - α 2 - ω 2 ) c - k 2 R C ( c ( c - 1 ) , ( c - α 2 ) ( c - ω 2 ) ) , 1 superscript 𝛼 2 elliptic-integral-third-kind-Pi italic-ϕ superscript 𝛼 2 𝑘 1 superscript 𝜔 2 elliptic-integral-third-kind-Pi italic-ϕ superscript 𝜔 2 𝑘 elliptic-integral-first-kind-F italic-ϕ 𝑘 1 superscript 𝛼 2 superscript 𝜔 2 𝑐 superscript 𝑘 2 Carlson-integral-RC 𝑐 𝑐 1 𝑐 superscript 𝛼 2 𝑐 superscript 𝜔 2 {\displaystyle{\displaystyle(1-\alpha^{2})\Pi\left(\phi,\alpha^{2},k\right)+(1% -\omega^{2})\Pi\left(\phi,\omega^{2},k\right)=F\left(\phi,k\right)+(1-\alpha^{% 2}-\omega^{2})\sqrt{c-k^{2}}\*R_{C}\left(c(c-1),(c-\alpha^{2})(c-\omega^{2})% \right),}}
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    DLMF:19.7.E10
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    ( k 2 - α 2 ) ( k 2 - ω 2 ) = k 2 ( k 2 - 1 ) superscript 𝑘 2 superscript 𝛼 2 superscript 𝑘 2 superscript 𝜔 2 superscript 𝑘 2 superscript 𝑘 2 1 {\displaystyle{\displaystyle(k^{2}-\alpha^{2})(k^{2}-\omega^{2})=k^{2}(k^{2}-1% )}}
    0 references