DLMF:19.25.E14 (Q6518): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of third kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of third kind / qualifier
 
test:

R J ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}

\CarlsonsymellintRJ@{\NVar{x}}{\NVar{y}}{\NVar{z}}{\NVar{p}}
Property / Symbols used: symmetric elliptic integral of third kind / qualifier
 
xml-id: C19.S16.E2.m2abdec

Revision as of 13:06, 2 January 2020

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DLMF:19.25.E14
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    Statements

    Π ( ϕ , α 2 , k ) - F ( ϕ , k ) = 1 3 α 2 R J ( c - 1 , c - k 2 , c , c - α 2 ) , elliptic-integral-third-kind-Pi italic-ϕ superscript 𝛼 2 𝑘 elliptic-integral-first-kind-F italic-ϕ 𝑘 1 3 superscript 𝛼 2 Carlson-integral-RJ 𝑐 1 𝑐 superscript 𝑘 2 𝑐 𝑐 superscript 𝛼 2 {\displaystyle{\displaystyle\Pi\left(\phi,\alpha^{2},k\right)-F\left(\phi,k% \right)=\tfrac{1}{3}\alpha^{2}R_{J}\left(c-1,c-k^{2},c,c-\alpha^{2}\right),}}
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    R J ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}
    C19.S16.E2.m2abdec
    0 references