DLMF:17.7.E17 (Q5413): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(One intermediate revision by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11713 / rank
 
Normal rank
Property / Symbols used: Q11713 / qualifier
 
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}}}}

\qmultiPochhammersym{\NVar{a_{1},a_{2},\dots,a_{r}}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11713 / qualifier
 
xml-id: C17.S2.SS1.p1.m6apdec
Property / Symbols used
 
Property / Symbols used: Q11710 / rank
 
Normal rank
Property / Symbols used: Q11710 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11710 / qualifier
 
xml-id: C17.S1.XMD10.m1pdec

Latest revision as of 15:03, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:17.7.E17
No description defined

    Statements

    Defining formula
    ϕ 7 8 ⁡ ( a , q ⁢ a 1 2 , - q ⁢ a 1 2 , b , c , d , e , f a 1 2 , - a 1 2 , a ⁢ q / b , a ⁢ q / c , a ⁢ q / d , a ⁢ q / e , a ⁢ q / f ; q , q ) - b a ⁢ ( a ⁢ q , c , d , e , f , b ⁢ q / a , b ⁢ q / c , b ⁢ q / d , b ⁢ q / e , b ⁢ q / f ; q ) ∞ ( a ⁢ q / b , a ⁢ q / c , a ⁢ q / d , a ⁢ q / e , a ⁢ q / f , b ⁢ c / a , b ⁢ d / a , b ⁢ e / a , b ⁢ f / a , b 2 ⁢ q / a ; q ) ∞ ⁢ ϕ 7 8 ⁡ ( b 2 / a , q ⁢ b ⁢ a - 1 2 , - q ⁢ b ⁢ a - 1 2 , b , b ⁢ c / a , b ⁢ d / a , b ⁢ e / a , b ⁢ f / a b ⁢ a - 1 2 , - b ⁢ a - 1 2 , b ⁢ q / a , b ⁢ q / c , b ⁢ q / d , b ⁢ q / e , b ⁢ q / f ; q , q ) = ( a ⁢ q , b / a , a ⁢ q / ( c ⁢ d ) , a ⁢ q / ( c ⁢ e ) , a ⁢ q / ( c ⁢ f ) , a ⁢ q / ( d ⁢ e ) , a ⁢ q / ( d ⁢ f ) , a ⁢ q / ( e ⁢ f ) ; q ) ∞ ( a ⁢ q / c , a ⁢ q / d , a ⁢ q / e , a ⁢ q / f , b ⁢ c / a , b ⁢ d / a , b ⁢ e / a , b ⁢ f / a ; q ) ∞ , q-hypergeometric-rphis 8 7 𝑎 𝑞 superscript 𝑎 1 2 𝑞 superscript 𝑎 1 2 𝑏 𝑐 𝑑 𝑒 𝑓 superscript 𝑎 1 2 superscript 𝑎 1 2 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑎 𝑞 𝑓 𝑞 𝑞 𝑏 𝑎 q-multiple-Pochhammer 𝑎 𝑞 𝑐 𝑑 𝑒 𝑓 𝑏 𝑞 𝑎 𝑏 𝑞 𝑐 𝑏 𝑞 𝑑 𝑏 𝑞 𝑒 𝑏 𝑞 𝑓 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑎 𝑞 𝑓 𝑏 𝑐 𝑎 𝑏 𝑑 𝑎 𝑏 𝑒 𝑎 𝑏 𝑓 𝑎 superscript 𝑏 2 𝑞 𝑎 𝑞 q-hypergeometric-rphis 8 7 superscript 𝑏 2 𝑎 𝑞 𝑏 superscript 𝑎 1 2 𝑞 𝑏 superscript 𝑎 1 2 𝑏 𝑏 𝑐 𝑎 𝑏 𝑑 𝑎 𝑏 𝑒 𝑎 𝑏 𝑓 𝑎 𝑏 superscript 𝑎 1 2 𝑏 superscript 𝑎 1 2 𝑏 𝑞 𝑎 𝑏 𝑞 𝑐 𝑏 𝑞 𝑑 𝑏 𝑞 𝑒 𝑏 𝑞 𝑓 𝑞 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑎 𝑎 𝑞 𝑐 𝑑 𝑎 𝑞 𝑐 𝑒 𝑎 𝑞 𝑐 𝑓 𝑎 𝑞 𝑑 𝑒 𝑎 𝑞 𝑑 𝑓 𝑎 𝑞 𝑒 𝑓 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑎 𝑞 𝑓 𝑏 𝑐 𝑎 𝑏 𝑑 𝑎 𝑏 𝑒 𝑎 𝑏 𝑓 𝑎 𝑞 {\displaystyle{\displaystyle{{}_{8}\phi_{7}}\left({a,qa^{\frac{1}{2}},-qa^{% \frac{1}{2}},b,c,d,e,f\atop a^{\frac{1}{2}},-a^{\frac{1}{2}},aq/b,aq/c,aq/d,aq% /e,aq/f};q,q\right)-\frac{b}{a}\frac{\left(aq,c,d,e,f,bq/a,bq/c,bq/d,bq/e,bq/f% ;q\right)_{\infty}}{\left(aq/b,aq/c,aq/d,aq/e,aq/f,bc/a,bd/a,be/a,bf/a,b^{2}q/% a;q\right)_{\infty}}\*{{}_{8}\phi_{7}}\left({b^{2}/a,qba^{-\frac{1}{2}},-qba^{% -\frac{1}{2}},b,bc/a,bd/a,be/a,bf/a\atop ba^{-\frac{1}{2}},-ba^{-\frac{1}{2}},% bq/a,bq/c,bq/d,bq/e,bq/f};q,q\right)=\frac{\left(aq,b/a,aq/(cd),aq/(ce),aq/(cf% ),aq/(de),aq/(df),aq/(ef);q\right)_{\infty}}{\left(aq/c,aq/d,aq/e,aq/f,bc/a,bd% /a,be/a,bf/a;q\right)_{\infty}},}}
    0 references
    DLMF id
    DLMF:17.7.E17
    0 references
    Symbols used
    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.m2apdec
    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.m6apdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1pdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5413&oldid=53789"