DLMF:17.10.E4 (Q5450): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: bilateral basic hypergeometric (or bilateral $$q$$ -hypergeometric) function / rank
 
Normal rank
Property / Symbols used: bilateral basic hypergeometric (or bilateral $$q$$ -hypergeometric) function / qualifier
 
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)}}

\qgenhyperpsi{\NVar{r}}{\NVar{s}}@{\NVar{a_{1},\dots,a_{r}}}{\NVar{b_{1},\dots,b_{s}}}{\NVar{q}}{\NVar{z}}
Property / Symbols used: bilateral basic hypergeometric (or bilateral $$q$$ -hypergeometric) function / qualifier
 
xml-id: C17.S4.E3.m2acdec

Revision as of 15:08, 2 January 2020

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DLMF:17.10.E4
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    Statements

    Defining formula
    ψ 2 2 ⁡ ( e , f a ⁢ q / c , a ⁢ q / d ; q , a ⁢ q e ⁢ f ) = ( q / c , q / d , a ⁢ q / e , a ⁢ q / f ; q ) ∞ ( a ⁢ q , q / a , a ⁢ q / ( c ⁢ d ) , a ⁢ q / ( e ⁢ f ) ; q ) ∞ ⁢ ∑ n = - ∞ ∞ ( 1 - a ⁢ q 2 ⁢ n ) ⁢ ( c , d , e , f ; q ) n ( 1 - a ) ⁢ ( a ⁢ q / c , a ⁢ q / d , a ⁢ q / e , a ⁢ q / f ; q ) n ⁢ ( q ⁢ a 3 c ⁢ d ⁢ e ⁢ f ) n ⁢ q n 2 . q-hypergeometric-rpsis 2 2 𝑒 𝑓 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑞 𝑎 𝑞 𝑒 𝑓 q-multiple-Pochhammer 𝑞 𝑐 𝑞 𝑑 𝑎 𝑞 𝑒 𝑎 𝑞 𝑓 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑞 𝑎 𝑎 𝑞 𝑐 𝑑 𝑎 𝑞 𝑒 𝑓 𝑞 superscript subscript 𝑛 1 𝑎 superscript 𝑞 2 𝑛 q-multiple-Pochhammer 𝑐 𝑑 𝑒 𝑓 𝑞 𝑛 1 𝑎 q-multiple-Pochhammer 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑎 𝑞 𝑓 𝑞 𝑛 superscript 𝑞 superscript 𝑎 3 𝑐 𝑑 𝑒 𝑓 𝑛 superscript 𝑞 superscript 𝑛 2 {\displaystyle{\displaystyle{{}_{2}\psi_{2}}\left({e,f\atop aq/c,aq/d};q,\frac% {aq}{ef}\right)=\frac{\left(q/c,q/d,aq/e,aq/f;q\right)_{\infty}}{\left(aq,q/a,% aq/(cd),aq/(ef);q\right)_{\infty}}\*\sum_{n=-\infty}^{\infty}\frac{(1-aq^{2n})% \left(c,d,e,f;q\right)_{n}}{(1-a)\left(aq/c,aq/d,aq/e,aq/f;q\right)_{n}}\left(% \frac{qa^{3}}{cdef}\right)^{n}q^{n^{2}}.}}
    0 references
    DLMF id
    DLMF:17.10.E4
    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.m2acdec
    0 references
     
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