DLMF:19.30.E3 (Q6676): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: elliptic integral symmetric in only two variables / rank
 
Normal rank
Property / Symbols used: elliptic integral symmetric in only two variables / qualifier
 
test:

R D ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}

\CarlsonsymellintRD@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: elliptic integral symmetric in only two variables / qualifier
 
xml-id: C19.S16.E5.m2adec

Revision as of 13:22, 2 January 2020

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DLMF:19.30.E3
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    Statements

    s / a = E ( ϕ , k ) = R F ( c - 1 , c - k 2 , c ) - 1 3 k 2 R D ( c - 1 , c - k 2 , c ) , 𝑠 𝑎 elliptic-integral-second-kind-E italic-ϕ 𝑘 Carlson-integral-RF 𝑐 1 𝑐 superscript 𝑘 2 𝑐 1 3 superscript 𝑘 2 Carlson-integral-RD 𝑐 1 𝑐 superscript 𝑘 2 𝑐 {\displaystyle{\displaystyle s/a=E\left(\phi,k\right)={R_{F}\left(c-1,c-k^{2},% c\right)-\tfrac{1}{3}k^{2}R_{D}\left(c-1,c-k^{2},c\right)},}}
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    R D ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    C19.S16.E5.m2adec
    0 references