DLMF:19.21.E12 (Q6430): 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 first kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of first kind / qualifier
 
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)}}

\CarlsonsymellintRF@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: symmetric elliptic integral of first kind / qualifier
 
xml-id: C19.S16.E1.m2ajdec

Revision as of 13:59, 2 January 2020

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DLMF:19.21.E12
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    Statements

    Defining formula
    ( p - x ) ⁢ R J ⁡ ( x , y , z , p ) + ( q - x ) ⁢ R J ⁡ ( x , y , z , q ) = 3 ⁢ R F ⁡ ( x , y , z ) - 3 ⁢ R C ⁡ ( ξ , η ) , 𝑝 𝑥 Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 𝑞 𝑥 Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑞 3 Carlson-integral-RF 𝑥 𝑦 𝑧 3 Carlson-integral-RC 𝜉 𝜂 {\displaystyle{\displaystyle(p-x)R_{J}\left(x,y,z,p\right)+(q-x)R_{J}\left(x,y% ,z,q\right)=3R_{F}\left(x,y,z\right)-3R_{C}\left(\xi,\eta\right),}}
    0 references
    DLMF id
    DLMF:19.21.E12
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    Defining formula
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2adec
    0 references
    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.m2ajdec
    0 references
     
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