DLMF:35.8.E11 (Q9833): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: generalized hypergeometric function of matrix argument / rank
 
Normal rank
Property / Symbols used: generalized hypergeometric function of matrix argument / qualifier
 
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)}}

\genhyperFmat{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{\mathbf{T}}}
Property / Symbols used: generalized hypergeometric function of matrix argument / qualifier
 
xml-id: C35.S8.E1.m2ajdec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
Defining formula:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2abdec
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.m1hdec
Property / Symbols used
 
Property / Symbols used: Q12724 / rank
 
Normal rank
Property / Symbols used: Q12724 / qualifier
 
Defining formula:

𝐓 𝐓 {\displaystyle{\displaystyle\mathbf{T}}}

\mathbf{T}
Property / Symbols used: Q12724 / qualifier
 
xml-id: C35.S1.XMD11.m1fdec
Property / Symbols used
 
Property / Symbols used: Q12732 / rank
 
Normal rank
Property / Symbols used: Q12732 / qualifier
 
Defining formula:

𝐎 ⁢ ( m ) 𝐎 𝑚 {\displaystyle{\displaystyle\mathbf{O}(m)}}

\mathbf{O}(m)
Property / Symbols used: Q12732 / qualifier
 
xml-id: C35.S1.XMD16.m1dec
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.m1hdec
Property / Symbols used
 
Property / Symbols used: Q12739 / rank
 
Normal rank
Property / Symbols used: Q12739 / qualifier
 
Defining formula:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q12739 / qualifier
 
xml-id: C35.S1.XMD6.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12740 / rank
 
Normal rank
Property / Symbols used: Q12740 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q12740 / qualifier
 
xml-id: C35.S1.XMD7.m1ddec
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.m1ddec

Latest revision as of 15:01, 2 January 2020

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DLMF:35.8.E11
No description defined

    Statements

    Defining formula
    F q p ⁡ ( a 1 , … , a p b 1 , … , b q ; 𝐇𝐓𝐇 - 1 ) = 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 superscript 𝐇𝐓𝐇 1 Gauss-hypergeometric-of-matrix-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝐓 {\displaystyle{\displaystyle{{}_{p}F_{q}}\left({a_{1},\dots,a_{p}\atop b_{1},% \dots,b_{q}};\mathbf{H}\mathbf{T}\mathbf{H}^{-1}\right)={{}_{p}F_{q}}\left({a_% {1},\dots,a_{p}\atop b_{1},\dots,b_{q}};\mathbf{T}\right),}}
    0 references
    DLMF id
    DLMF:35.8.E11
    0 references
    constraint
    𝐇 ∈ 𝐎 ⁢ ( m ) 𝐇 𝐎 𝑚 {\displaystyle{\displaystyle\mathbf{H}\in\mathbf{O}(m)}}
    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.m2ajdec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2abdec
    0 references
    Q12726
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C35.S1.XMD1.m1hdec
    0 references
    Q12724
    Defining formula
    𝐓 𝐓 {\displaystyle{\displaystyle\mathbf{T}}}
    xml-id
    C35.S1.XMD11.m1fdec
    0 references
    Q12732
    Defining formula
    𝐎 ⁢ ( m ) 𝐎 𝑚 {\displaystyle{\displaystyle\mathbf{O}(m)}}
    xml-id
    C35.S1.XMD16.m1dec
    0 references
    Q12728
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C35.S1.XMD2.m1hdec
    0 references
    Q12739
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C35.S1.XMD6.m1ddec
    0 references
    Q12740
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C35.S1.XMD7.m1ddec
    0 references
    Q12723
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C35.S1.XMD8.m1ddec
    0 references
     
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