DLMF:19.21.E15 (Q6435): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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
 
Defining formula:

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

Latest revision as of 13:59, 2 January 2020

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DLMF:19.21.E15
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    Statements

    Defining formula
    p ⁢ R J ⁡ ( 0 , y , z , p ) + q ⁢ R J ⁡ ( 0 , y , z , q ) = 3 ⁢ R F ⁡ ( 0 , y , z ) , 𝑝 Carlson-integral-RJ 0 𝑦 𝑧 𝑝 𝑞 Carlson-integral-RJ 0 𝑦 𝑧 𝑞 3 Carlson-integral-RF 0 𝑦 𝑧 {\displaystyle{\displaystyle pR_{J}\left(0,y,z,p\right)+qR_{J}\left(0,y,z,q% \right)=3R_{F}\left(0,y,z\right),}}
    0 references
    DLMF id
    DLMF:19.21.E15
    0 references
    constraint
    p ⁢ q = y ⁢ z 𝑝 𝑞 𝑦 𝑧 {\displaystyle{\displaystyle pq=yz}}
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2akdec
    0 references
    symmetric elliptic integral of third kind
    Defining formula
    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)}}
    xml-id
    C19.S16.E2.m2abdec
    0 references
     
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