DLMF:35.8.E1 (Q9823)

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DLMF:35.8.E1
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    Statements

    Defining formula
    F q p ⁡ ( a 1 , … , a p b 1 , … , b q ; 𝐓 ) = ∑ k = 0 ∞ 1 k ! ⁢ ∑ | κ | = k [ a 1 ] κ ⁢ ⋯ ⁢ [ a p ] κ [ b 1 ] κ ⁢ ⋯ ⁢ [ b q ] κ ⁢ Z κ ⁡ ( 𝐓 ) . Gauss-hypergeometric-of-matrix-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝐓 superscript subscript 𝑘 0 1 𝑘 subscript 𝜅 𝑘 shifted-factorial subscript 𝑎 1 𝜅 ⋯ shifted-factorial subscript 𝑎 𝑝 𝜅 shifted-factorial subscript 𝑏 1 𝜅 ⋯ shifted-factorial subscript 𝑏 𝑞 𝜅 zonal-polynomial 𝜅 𝐓 {\displaystyle{\displaystyle{{}_{p}F_{q}}\left({a_{1},\dots,a_{p}\atop b_{1},% \dots,b_{q}};\mathbf{T}\right)=\sum_{k=0}^{\infty}\frac{1}{k!}\sum_{|\kappa|=k% }\frac{{\left[a_{1}\right]_{\kappa}}\cdots{\left[a_{p}\right]_{\kappa}}}{{% \left[b_{1}\right]_{\kappa}}\cdots{\left[b_{q}\right]_{\kappa}}}Z_{\kappa}% \left(\mathbf{T}\right).}}
    0 references
    DLMF id
    DLMF:35.8.E1
    0 references
    Symbols used
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    partitional shifted factorial
    Defining formula
    [ a ] κ shifted-factorial 𝑎 𝜅 {\displaystyle{\displaystyle{\left[\NVar{a}\right]_{\NVar{\kappa}}}}}
    xml-id
    C35.S4.E1.m2adec
    0 references
    Q12730
    Defining formula
    Z κ ⁡ ( 𝐓 ) zonal-polynomial 𝜅 𝐓 {\displaystyle{\displaystyle Z_{\NVar{\kappa}}\left(\NVar{\mathbf{T}}\right)}}
    xml-id
    C35.S4.SS1.p3.m3adec
    0 references
    Q12726
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C35.S1.XMD1.m1dec
    0 references
    Q12724
    Defining formula
    𝐓 𝐓 {\displaystyle{\displaystyle\mathbf{T}}}
    xml-id
    C35.S1.XMD11.m1dec
    0 references
    Q12728
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C35.S1.XMD2.m1dec
    0 references
    Q12729
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C35.S1.XMD5.m1dec
    0 references
    Q12739
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C35.S1.XMD6.m1dec
    0 references
    Q12740
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C35.S1.XMD7.m1dec
    0 references
     
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