DLMF:16.11.E7 (Q5241): 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: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2abdec

Revision as of 14:38, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:16.11.E7
No description defined

    Statements

    ( = 1 q Γ ( a ) / = 1 q Γ ( b ) ) F q q ( a 1 , , a q b 1 , , b q ; z ) H q , q ( z e π i ) + E q , q ( z ) . asymptotic-expansion superscript subscript product 1 𝑞 Euler-Gamma subscript 𝑎 superscript subscript product 1 𝑞 Euler-Gamma subscript 𝑏 Gauss-hypergeometric-pFq 𝑞 𝑞 subscript 𝑎 1 subscript 𝑎 𝑞 subscript 𝑏 1 subscript 𝑏 𝑞 𝑧 subscript 𝐻 𝑞 𝑞 𝑧 minus-or-plus 𝜋 imaginary-unit subscript 𝐸 𝑞 𝑞 𝑧 {\displaystyle{\displaystyle\left({\textstyle\ifrac{\prod\limits_{\ell=1}^{q}% \Gamma\left(a_{\ell}\right)}{\prod\limits_{\ell=1}^{q}\Gamma\left(b_{\ell}% \right)}}\right){{}_{q}F_{q}}\left({a_{1},\dots,a_{q}\atop b_{1},\dots,b_{q}};% z\right)\sim H_{q,q}(z{\mathrm{e}^{\mp\pi\mathrm{i}}})+E_{q,q}(z).}}
    0 references
    DLMF:16.11.E7
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2abdec
    0 references