DLMF:19.25.E43 (Q6551): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: multivariate hypergeometric function / rank
 
Normal rank
Property / Symbols used: multivariate hypergeometric function / qualifier
 
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)}}

\Carlsonmultivarhyper{\NVar{-a}}@{\NVar{b_{1}},\dots,\NVar{b_{n}}}{\NVar{z_{1}},\dots,\NVar{z_{n}}}
Property / Symbols used: multivariate hypergeometric function / qualifier
 
xml-id: C19.S16.E9.m2addec
Property / Symbols used
 
Property / Symbols used: Q11581 / rank
 
Normal rank
Property / Symbols used: Q11581 / qualifier
 
Defining formula:

F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}

\genhyperF{2}{1}@{\NVar{a},\NVar{b}}{\NVar{c}}{\NVar{z}}
Property / Symbols used: Q11581 / qualifier
 
xml-id: C16.S2.m5aadec

Latest revision as of 14:10, 2 January 2020

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DLMF:19.25.E43
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    Statements

    Defining formula
    R - a ⁡ ( b 1 , b 2 ; z 1 , z 2 ) = z 2 - a ⁢ F 1 2 ⁡ ( a , b 1 ; b 1 + b 2 ; 1 - ( z 1 / z 2 ) ) . Carlson-integral-R 𝑎 subscript 𝑏 1 subscript 𝑏 2 subscript 𝑧 1 subscript 𝑧 2 superscript subscript 𝑧 2 𝑎 Gauss-hypergeometric-F-as-2F1 𝑎 subscript 𝑏 1 subscript 𝑏 1 subscript 𝑏 2 1 subscript 𝑧 1 subscript 𝑧 2 {\displaystyle{\displaystyle R_{-a}\left(b_{1},b_{2};z_{1},z_{2}\right)=z_{2}^% {-a}{{}_{2}F_{1}}\left(a,b_{1};b_{1}+b_{2};1-(z_{1}/z_{2})\right).}}
    0 references
    DLMF id
    DLMF:19.25.E43
    0 references
    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.m2addec
    0 references
    Q11581
    Defining formula
    F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}
    xml-id
    C16.S2.m5aadec
    0 references
     
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