DLMF:19.20.E23 (Q6414): Difference between revisions

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

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.m2ahdec

Latest revision as of 13:58, 2 January 2020

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DLMF:19.20.E23
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    Statements

    Defining formula
    R D ⁡ ( x , y , a ) = R - 3 4 ⁡ ( 5 4 , 1 2 ; a 2 , x ⁢ y ) , Carlson-integral-RD 𝑥 𝑦 𝑎 Carlson-integral-R 3 4 5 4 1 2 superscript 𝑎 2 𝑥 𝑦 {\displaystyle{\displaystyle R_{D}\left(x,y,a\right)=R_{-\frac{3}{4}}\left(% \tfrac{5}{4},\tfrac{1}{2};a^{2},xy\right),}}
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    DLMF id
    DLMF:19.20.E23
    0 references
    constraint
    a = 1 2 ⁢ x + 1 2 ⁢ y 𝑎 1 2 𝑥 1 2 𝑦 {\displaystyle{\displaystyle a=\tfrac{1}{2}x+\tfrac{1}{2}y}}
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    Symbols used
    multivariate hypergeometric function
    Defining formula
    R - a ⁡ ( b 1 , … , b n ; z 1 , … , z n ) Carlson-integral-R 𝑎 subscript 𝑏 1 … subscript 𝑏 𝑛 subscript 𝑧 1 … subscript 𝑧 𝑛 {\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}% };\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}
    xml-id
    C19.S16.E9.m2aadec
    0 references
    elliptic integral symmetric in only two variables
    Defining formula
    R D ⁡ ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E5.m2ahdec
    0 references
     
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