DLMF:16.8.E10 (Q5229): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11125 / rank
 
Normal rank
Property / Symbols used: Q11125 / qualifier
 
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)}}

\genhyperF{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{z}}
Property / Symbols used: Q11125 / qualifier
 
xml-id: C16.S2.m1addec

Revision as of 14:36, 2 January 2020

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DLMF:16.8.E10
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    Statements

    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:16.8.E10
    0 references
    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)}}
    C16.S2.m1addec
    0 references