DLMF:16.8.E11 (Q5230): Difference between revisions

From DRMF
Jump to navigation Jump to search
Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
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.m1aedec

Revision as of 14:36, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:16.8.E11
No description defined

    Statements

    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
    DLMF:16.8.E11
    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.m1aedec
    0 references