DLMF:17.8.E2 (Q5421): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11718 / rank
 
Normal rank
Property / Symbols used: Q11718 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11718 / qualifier
 
xml-id: C17.S1.XMD7.m1adec

Latest revision as of 15:04, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:17.8.E2
No description defined

    Statements

    Defining formula
    ψ 1 1 ⁡ ( a b ; q , z ) = ( q , b / a , a ⁢ z , q / ( a ⁢ z ) ; q ) ∞ ( b , q / a , z , b / ( a ⁢ z ) ; q ) ∞ . q-hypergeometric-rpsis 1 1 𝑎 𝑏 𝑞 𝑧 q-multiple-Pochhammer 𝑞 𝑏 𝑎 𝑎 𝑧 𝑞 𝑎 𝑧 𝑞 q-multiple-Pochhammer 𝑏 𝑞 𝑎 𝑧 𝑏 𝑎 𝑧 𝑞 {\displaystyle{\displaystyle{{}_{1}\psi_{1}}\left({a\atop b};q,z\right)=\frac{% \left(q,b/a,az,q/(az);q\right)_{\infty}}{\left(b,q/a,z,b/(az);q\right)_{\infty% }}.}}
    0 references
    DLMF id
    DLMF:17.8.E2
    0 references
    Symbols used
    bilateral basic hypergeometric (or bilateral $$q$$ -hypergeometric) function
    Defining formula
    ψ s r ⁡ ( a 1 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rpsis 𝑟 𝑠 subscript 𝑎 1 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r}}\psi_{\NVar{s}}}\left(\NVar{a_{1},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
    xml-id
    C17.S4.E3.m2adec
    0 references
    Q11713
    Defining formula
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6aadec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1adec
    0 references
    Q11718
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5421&oldid=54017"