DLMF:17.6.E25 (Q5392)

From DRMF
Revision as of 15:00, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:17.6.E25
No description defined

    Statements

    Defining formula
    𝒟 q n ⁢ ϕ 1 2 ⁡ ( a , b c ; q , z ⁢ d ) = ( a , b ; q ) n ⁢ d n ( c ; q ) n ⁢ ( 1 - q ) n ⁢ ϕ 1 2 ⁡ ( a ⁢ q n , b ⁢ q n c ⁢ q n ; q , d ⁢ z ) , superscript subscript 𝒟 𝑞 𝑛 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 𝑑 q-multiple-Pochhammer 𝑎 𝑏 𝑞 𝑛 superscript 𝑑 𝑛 q-Pochhammer-symbol 𝑐 𝑞 𝑛 superscript 1 𝑞 𝑛 q-hypergeometric-rphis 2 1 𝑎 superscript 𝑞 𝑛 𝑏 superscript 𝑞 𝑛 𝑐 superscript 𝑞 𝑛 𝑞 𝑑 𝑧 {\displaystyle{\displaystyle\mathcal{D}_{q}^{n}{{}_{2}\phi_{1}}\left({a,b\atop c% };q,zd\right)=\frac{\left(a,b;q\right)_{n}d^{n}}{\left(c;q\right)_{n}(1-q)^{n}% }{{}_{2}\phi_{1}}\left({aq^{n},bq^{n}\atop cq^{n}};q,dz\right),}}
    0 references
    DLMF id
    DLMF:17.6.E25
    0 references
    Symbols used
    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.m2aidec
    0 references
    basic hypergeometric (or $$q$$ -hypergeometric) function
    Defining formula
    ϕ s r + 1 ⁡ ( a 0 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rphis 𝑟 1 𝑠 subscript 𝑎 0 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
    xml-id
    C17.S4.E1.m2axdec
    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.m6amdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1xdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5392&oldid=53229"