DLMF:16.8.E10 (Q5229)

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DLMF:16.8.E10
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    Statements

    Defining formula
    lim | α | → ∞ ⁡ F q p + 1 ⁡ ( a 1 , … , a p , α b 1 , … , b q ; z α ) = F q p ⁡ ( a 1 , … , a p b 1 , … , b q ; z ) . subscript → 𝛼 Gauss-hypergeometric-pFq 𝑝 1 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 𝛼 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 𝛼 Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle\lim_{|\alpha|\to\infty}{{}_{p+1}F_{q}}\left({a_{1% },\dots,a_{p},\alpha\atop b_{1},\dots,b_{q}};\frac{z}{\alpha}\right)={{}_{p}F_% {q}}\left({a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}};z\right).}}
    0 references
    DLMF id
    DLMF:16.8.E10
    0 references
    Symbols used
    Q11125
    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.m1addec
    0 references
    Q11690
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C16.S1.XMD1.m1ddec
    0 references
    Q11691
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C16.S1.XMD2.m1gdec
    0 references
     
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