DLMF:35.8.E10 (Q9832)

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DLMF:35.8.E10
No description defined

    Statements

    Defining formula
    lim γ → ∞ ⁡ F q + 1 p ⁡ ( a 1 , … , a p b 1 , … , b q , γ ; γ ⁢ 𝐓 ) = F q p ⁡ ( a 1 , … , a p b 1 , … , b q ; 𝐓 ) . subscript → 𝛾 Gauss-hypergeometric-of-matrix-pFq 𝑝 𝑞 1 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝛾 𝛾 𝐓 Gauss-hypergeometric-of-matrix-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝐓 {\displaystyle{\displaystyle\lim_{\gamma\to\infty}{{}_{p}F_{q+1}}\left({a_{1},% \dots,a_{p}\atop b_{1},\dots,b_{q},\gamma};\gamma\mathbf{T}\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.E10
    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.m2aidec
    0 references
    Q12726
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C35.S1.XMD1.m1gdec
    0 references
    Q12724
    Defining formula
    𝐓 𝐓 {\displaystyle{\displaystyle\mathbf{T}}}
    xml-id
    C35.S1.XMD11.m1edec
    0 references
    Q12728
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C35.S1.XMD2.m1gdec
    0 references
    Q12739
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C35.S1.XMD6.m1cdec
    0 references
    Q12740
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C35.S1.XMD7.m1cdec
    0 references
     
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