DLMF:16.16.E6 (Q5272): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: fourth Appell function / rank
 
Normal rank
Property / Symbols used: fourth Appell function / qualifier
 
test:

F 4 ⁡ ( α , β ; γ , γ ′ ⁢ missing ⁢ missing ; missing , missing ) Appell-F-4 𝛼 𝛽 𝛾 superscript 𝛾 ′ missing missing {\displaystyle{\displaystyle{F_{4}}\left(\NVar{\alpha},\NVar{\beta};\NVar{% \gamma},\NVar{\gamma^{\prime}}{missing}{missing};missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}

\AppellF{4}@{\NVar{\alpha}}{\NVar{\beta}}{\NVar{\gamma}}{\NVar{\gamma^{\prime}% }}{\NVar{x}}{\NVar{y}}
Property / Symbols used: fourth Appell function / qualifier
 
xml-id: C16.S13.E4.m2adec
Property / Symbols used
 
Property / Symbols used: Q11581 / rank
 
Normal rank
Property / Symbols used: Q11581 / qualifier
 
test:

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.m5acdec

Latest revision as of 13:42, 2 January 2020

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DLMF:16.16.E6
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    Statements

    test
    F 4 ⁡ ( α , β ; γ , α + β - γ + 1 ; x ⁢ ( 1 - y ) , y ⁢ ( 1 - x ) ) = F 1 2 ⁡ ( α , β γ ; x ) ⁢ F 1 2 ⁡ ( α , β α + β - γ + 1 ; y ) . Appell-F-4 𝛼 𝛽 𝛾 𝛼 𝛽 𝛾 1 𝑥 1 𝑦 𝑦 1 𝑥 Gauss-hypergeometric-F-as-2F1 𝛼 𝛽 𝛾 𝑥 Gauss-hypergeometric-F-as-2F1 𝛼 𝛽 𝛼 𝛽 𝛾 1 𝑦 {\displaystyle{\displaystyle{F_{4}}\left(\alpha,\beta;\gamma,\alpha+\beta-% \gamma+1;x(1-y),y(1-x)\right)={{}_{2}F_{1}}\left({\alpha,\beta\atop\gamma};x% \right){{}_{2}F_{1}}\left({\alpha,\beta\atop\alpha+\beta-\gamma+1};y\right).}}
    0 references
    DLMF id
    DLMF:16.16.E6
    0 references
    Symbols used
    fourth Appell function
    test
    F 4 ⁡ ( α , β ; γ , γ ′ ⁢ missing ⁢ missing ; missing , missing ) Appell-F-4 𝛼 𝛽 𝛾 superscript 𝛾 ′ missing missing {\displaystyle{\displaystyle{F_{4}}\left(\NVar{\alpha},\NVar{\beta};\NVar{% \gamma},\NVar{\gamma^{\prime}}{missing}{missing};missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C16.S13.E4.m2adec
    0 references
    Q11581
    test
    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.m5acdec
    0 references
     
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