DLMF:35.6.E1 (Q9802)

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DLMF:35.6.E1
No description defined

    Statements

    Defining formula
    F 1 1 ⁥ ( a b ; 𝐓 ) = ∑ k = 0 ∞ 1 k ! ⁹ ∑ | Îș | = k [ a ] Îș [ b ] Îș ⁹ Z Îș ⁥ ( 𝐓 ) . Gauss-hypergeometric-of-matrix-pFq 1 1 𝑎 𝑏 𝐓 superscript subscript 𝑘 0 1 𝑘 subscript 𝜅 𝑘 shifted-factorial 𝑎 𝜅 shifted-factorial 𝑏 𝜅 zonal-polynomial 𝜅 𝐓 {\displaystyle{\displaystyle{{}_{1}F_{1}}\left({a\atop b};\mathbf{T}\right)=% \sum_{k=0}^{\infty}\frac{1}{k!}\sum_{|\kappa|=k}\frac{{\left[a\right]_{\kappa}% }}{{\left[b\right]_{\kappa}}}Z_{\kappa}\left(\mathbf{T}\right).}}
    0 references
    DLMF id
    DLMF:35.6.E1
    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.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    partitional shifted factorial
    Defining formula
    [ a ] Îș shifted-factorial 𝑎 𝜅 {\displaystyle{\displaystyle{\left[\NVar{a}\right]_{\NVar{\kappa}}}}}
    xml-id
    C35.S4.E1.m2adec
    0 references
    Q12730
    Defining formula
    Z Îș ⁥ ( 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
     
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