DLMF:17.11.E3 (Q5455)

From DRMF
Revision as of 16:00, 29 December 2019 by Admin (talk | contribs) (‎Created a new Item: Wikidata Toolkit example test item creation)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:17.11.E3
No description defined

    Statements

    Defining formula
    Φ ( 3 ) ⁡ ( a , a ′ ; b , b ′ ; c ; q ; x , y ) = ( a , b ⁢ x ; q ) ∞ ( c , x ; q ) ∞ ⁢ ∑ n , r ≧ 0 ( a ′ , b ′ ; q ) n ⁢ ( x ; q ) r ⁢ ( c / a ; q ) n + r ⁢ a r ⁢ y n ( q , c / a ; q ) n ⁢ ( q , b ⁢ x ; q ) r . q-Appell-Phi-3 𝑎 superscript 𝑎 ′ 𝑏 superscript 𝑏 ′ 𝑐 𝑞 𝑥 𝑦 q-multiple-Pochhammer 𝑎 𝑏 𝑥 𝑞 q-multiple-Pochhammer 𝑐 𝑥 𝑞 subscript 𝑛 𝑟 0 q-multiple-Pochhammer superscript 𝑎 ′ superscript 𝑏 ′ 𝑞 𝑛 q-Pochhammer-symbol 𝑥 𝑞 𝑟 q-Pochhammer-symbol 𝑐 𝑎 𝑞 𝑛 𝑟 superscript 𝑎 𝑟 superscript 𝑦 𝑛 q-multiple-Pochhammer 𝑞 𝑐 𝑎 𝑞 𝑛 q-multiple-Pochhammer 𝑞 𝑏 𝑥 𝑞 𝑟 {\displaystyle{\displaystyle\Phi^{(3)}\left(a,a^{\prime};b,b^{\prime};c;q;x,y% \right)=\frac{\left(a,bx;q\right)_{\infty}}{\left(c,x;q\right)_{\infty}}\sum_{% n,r\geqq 0}\frac{\left(a^{\prime},b^{\prime};q\right)_{n}\left(x;q\right)_{r}% \left(c/a;q\right)_{n+r}a^{r}y^{n}}{\left(q,c/a;q\right)_{n}\left(q,bx;q\right% )_{r}}.}}
    0 references
    DLMF id
    DLMF:17.11.E3
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5455&oldid=11454"