DLMF:16.8.E8 (Q5227): 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 / constraint
 

| ph ( - z ) | π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\pi}}

|\phase@{-z}|\leq\pi
Property / constraint: | ph ( - z ) | π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\pi}} / rank
 
Normal rank

Revision as of 17:58, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:16.8.E8
No description defined

    Statements

    F q q + 1 ( a 1 , , a q + 1 b 1 , , b q ; z ) = j = 1 q + 1 ( k = 1 k j q + 1 Γ ( a k - a j ) Γ ( a k ) / k = 1 q Γ ( b k - a j ) Γ ( b k ) ) w ~ j ( z ) , Gauss-hypergeometric-pFq 𝑞 1 𝑞 subscript 𝑎 1 subscript 𝑎 𝑞 1 subscript 𝑏 1 subscript 𝑏 𝑞 𝑧 superscript subscript 𝑗 1 𝑞 1 superscript subscript product 𝑘 1 𝑘 𝑗 𝑞 1 Euler-Gamma subscript 𝑎 𝑘 subscript 𝑎 𝑗 Euler-Gamma subscript 𝑎 𝑘 superscript subscript product 𝑘 1 𝑞 Euler-Gamma subscript 𝑏 𝑘 subscript 𝑎 𝑗 Euler-Gamma subscript 𝑏 𝑘 subscript ~ 𝑤 𝑗 𝑧 {\displaystyle{\displaystyle{{}_{q+1}F_{q}}\left({a_{1},\dots,a_{q+1}\atop b_{% 1},\dots,b_{q}};z\right)=\sum_{j=1}^{q+1}\left({\textstyle\ifrac{\prod\limits_% {\begin{subarray}{c}k=1\\ k\neq j\end{subarray}}^{q+1}\frac{\Gamma\left(a_{k}-a_{j}\right)}{\Gamma\left(% a_{k}\right)}}{\prod\limits_{k=1}^{q}\frac{\Gamma\left(b_{k}-a_{j}\right)}{% \Gamma\left(b_{k}\right)}}}\right)\widetilde{w}_{j}(z),}}
    0 references
    DLMF:16.8.E8
    0 references
    | ph ( - z ) | π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\pi}}
    0 references