DLMF:17.8.E5 (Q5424): Difference between revisions

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‎Changed an Item: Add constraint
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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.m6addec

Revision as of 15:05, 2 January 2020

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DLMF:17.8.E5
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    Statements

    Defining formula
    ψ 3 3 ⁡ ( b , c , d q / b , q / c , q / d ; q , q b ⁢ c ⁢ d ) = ( q , q / ( b ⁢ c ) , q / ( b ⁢ d ) , q / ( c ⁢ d ) ; q ) ∞ ( q / b , q / c , q / d , q / ( b ⁢ c ⁢ d ) ; q ) ∞ , q-hypergeometric-rpsis 3 3 𝑏 𝑐 𝑑 𝑞 𝑏 𝑞 𝑐 𝑞 𝑑 𝑞 𝑞 𝑏 𝑐 𝑑 q-multiple-Pochhammer 𝑞 𝑞 𝑏 𝑐 𝑞 𝑏 𝑑 𝑞 𝑐 𝑑 𝑞 q-multiple-Pochhammer 𝑞 𝑏 𝑞 𝑐 𝑞 𝑑 𝑞 𝑏 𝑐 𝑑 𝑞 {\displaystyle{\displaystyle{{}_{3}\psi_{3}}\left({b,c,d\atop q/b,q/c,q/d};q,% \frac{q}{bcd}\right)=\frac{\left(q,q/(bc),q/(bd),q/(cd);q\right)_{\infty}}{% \left(q/b,q/c,q/d,q/(bcd);q\right)_{\infty}},}}
    0 references
    DLMF id
    DLMF:17.8.E5
    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.m2abdec
    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.m6addec
    0 references
     
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