DLMF:35.8.E6 (Q9828): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12725 / rank
 
Normal rank
Property / Symbols used: Q12725 / qualifier
 
Defining formula:

Γ m ⁡ ( a ) multivariate-Euler-Gamma 𝑚 𝑎 {\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}

\multivarEulerGamma{\NVar{m}}@{\NVar{a}}
Property / Symbols used: Q12725 / qualifier
 
xml-id: C35.S3.SS1.m1abdec
Property / Symbols used
 
Property / Symbols used: Q12726 / rank
 
Normal rank
Property / Symbols used: Q12726 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12726 / qualifier
 
xml-id: C35.S1.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12728 / rank
 
Normal rank
Property / Symbols used: Q12728 / qualifier
 
Defining formula:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q12728 / qualifier
 
xml-id: C35.S1.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12723 / rank
 
Normal rank
Property / Symbols used: Q12723 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12723 / qualifier
 
xml-id: C35.S1.XMD8.m1bdec

Latest revision as of 15:00, 2 January 2020

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DLMF:35.8.E6
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    Statements

    Defining formula
    F 2 3 ⁡ ( a 1 , a 2 , a 3 b 1 , b 2 ; 𝐈 ) = Γ m ⁡ ( b 1 - a 1 ) ⁢ Γ m ⁡ ( b 1 - a 2 ) Γ m ⁡ ( b 1 ) ⁢ Γ m ⁡ ( b 1 - a 1 - a 2 ) ⁢ Γ m ⁡ ( b 1 - a 3 ) ⁢ Γ m ⁡ ( b 1 - a 1 - a 2 - a 3 ) Γ m ⁡ ( b 1 - a 1 - a 3 ) ⁢ Γ m ⁡ ( b 1 - a 2 - a 3 ) . Gauss-hypergeometric-of-matrix-pFq 3 2 subscript 𝑎 1 subscript 𝑎 2 subscript 𝑎 3 subscript 𝑏 1 subscript 𝑏 2 𝐈 multivariate-Euler-Gamma 𝑚 subscript 𝑏 1 subscript 𝑎 1 multivariate-Euler-Gamma 𝑚 subscript 𝑏 1 subscript 𝑎 2 multivariate-Euler-Gamma 𝑚 subscript 𝑏 1 multivariate-Euler-Gamma 𝑚 subscript 𝑏 1 subscript 𝑎 1 subscript 𝑎 2 multivariate-Euler-Gamma 𝑚 subscript 𝑏 1 subscript 𝑎 3 multivariate-Euler-Gamma 𝑚 subscript 𝑏 1 subscript 𝑎 1 subscript 𝑎 2 subscript 𝑎 3 multivariate-Euler-Gamma 𝑚 subscript 𝑏 1 subscript 𝑎 1 subscript 𝑎 3 multivariate-Euler-Gamma 𝑚 subscript 𝑏 1 subscript 𝑎 2 subscript 𝑎 3 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a_{1},a_{2},a_{3}\atop b_{1},b% _{2}};\mathbf{I}\right)=\frac{\Gamma_{m}\left(b_{1}-a_{1}\right)\Gamma_{m}% \left(b_{1}-a_{2}\right)}{\Gamma_{m}\left(b_{1}\right)\Gamma_{m}\left(b_{1}-a_% {1}-a_{2}\right)}\*\frac{\Gamma_{m}\left(b_{1}-a_{3}\right)\Gamma_{m}\left(b_{% 1}-a_{1}-a_{2}-a_{3}\right)}{\Gamma_{m}\left(b_{1}-a_{1}-a_{3}\right)\Gamma_{m% }\left(b_{1}-a_{2}-a_{3}\right)}.}}
    0 references
    DLMF id
    DLMF:35.8.E6
    0 references
    Symbols used
    generalized hypergeometric function of matrix argument
    Defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; 𝐓 ) Gauss-hypergeometric-of-matrix-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝐓 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{\mathbf{T}}\right)}}
    xml-id
    C35.S8.E1.m2aedec
    0 references
    Q12725
    Defining formula
    Γ m ⁡ ( a ) multivariate-Euler-Gamma 𝑚 𝑎 {\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}
    xml-id
    C35.S3.SS1.m1abdec
    0 references
    Q12726
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C35.S1.XMD1.m1cdec
    0 references
    Q12728
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C35.S1.XMD2.m1cdec
    0 references
    Q12723
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C35.S1.XMD8.m1bdec
    0 references
     
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