DLMF:17.6.E28 (Q5395): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11298 / rank
 
Normal rank
Property / Symbols used: Q11298 / qualifier
 
Defining formula:

( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

\qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11298 / qualifier
 
xml-id: C17.S2.SS1.p1.m2akdec

Revision as of 15:01, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:17.6.E28
No description defined

    Statements

    Defining formula
    ϕ 1 2 ⁡ ( q α , q β q γ ; q , z ) = Γ q ⁡ ( γ ) Γ q ⁡ ( β ) ⁢ Γ q ⁡ ( γ - β ) ⁢ ∫ 0 1 t β - 1 ⁢ ( t ⁢ q ; q ) γ - β - 1 ( x ⁢ t ; q ) α ⁢ d q t . q-hypergeometric-rphis 2 1 superscript 𝑞 𝛼 superscript 𝑞 𝛽 superscript 𝑞 𝛾 𝑞 𝑧 q-Gamma 𝑞 𝛾 q-Gamma 𝑞 𝛽 q-Gamma 𝑞 𝛾 𝛽 superscript subscript 0 1 superscript 𝑡 𝛽 1 q-Pochhammer-symbol 𝑡 𝑞 𝑞 𝛾 𝛽 1 q-Pochhammer-symbol 𝑥 𝑡 𝑞 𝛼 q-differential 𝑞 𝑡 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({q^{\alpha},q^{\beta}\atop q% ^{\gamma}};q,z\right)=\frac{\Gamma_{q}\left(\gamma\right)}{\Gamma_{q}\left(% \beta\right)\Gamma_{q}\left(\gamma-\beta\right)}\int_{0}^{1}\frac{t^{\beta-1}% \left(tq;q\right)_{\gamma-\beta-1}}{\left(xt;q\right)_{\alpha}}{\mathrm{d}}_{q% }t.}}
    0 references
    DLMF id
    DLMF:17.6.E28
    0 references
    Symbols used
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    $$q$$ -gamma function
    Defining formula
    Γ q ⁡ ( z ) q-Gamma 𝑞 𝑧 {\displaystyle{\displaystyle\Gamma_{\NVar{q}}\left(\NVar{z}\right)}}
    xml-id
    C5.S18.E4.m2adec
    0 references
    Q11298
    Defining formula
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2akdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5395&oldid=53331"