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DLMF:16.8.E11 - MaRDI portal

DLMF:16.8.E11 (Q5927)

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DLMF:16.8.E11
No description defined

    Statements

    DLMF defining formula
    lim | β | → ∞ ⁡ F q + 1 p ⁡ ( a 1 , … , a p b 1 , … , b q , β ; β ⁢ z ) = F q p ⁡ ( a 1 , … , a p b 1 , … , b q ; z ) , subscript → 𝛽 Gauss-hypergeometric-pFq 𝑝 𝑞 1 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝛽 𝛽 𝑧 Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle\lim_{|\beta|\to\infty}{{}_{p}F_{q+1}}\left({a_{1}% ,\dots,a_{p}\atop b_{1},\dots,b_{q},\beta};\beta z\right)={{}_{p}F_{q}}\left({% a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}};z\right),}}
    0 references
    Symbols used
    alternatively F q p ( a ; b ; z ) or F q p ( a b ; z ) generalized hypergeometric function
    DLMF defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1aedec
    0 references
    nonnegative integer
    DLMF defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C16.S1.XMD1.m1edec
    0 references
    nonnegative integer
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C16.S1.XMD2.m1hdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C16.S1.XMD3.m1jdec
    0 references
    real or complex parameters
    DLMF defining formula
    a , a 1 , … , a p 𝑎 subscript 𝑎 1 … subscript 𝑎 𝑝 {\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
    xml-id
    C16.S1.XMD4.m1fdec
    0 references
    real or complex parameters
    DLMF defining formula
    b , b 1 , … , b q 𝑏 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}
    xml-id
    C16.S1.XMD5.m1fdec
    0 references

    Identifiers

     
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