DLMF:17.6.E12 (Q5379): Difference between revisions

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Property / constraint
 

| z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}

|z|<1
Property / constraint: | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}} / rank
 
Normal rank

Revision as of 16:59, 30 December 2019

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DLMF:17.6.E12
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    Statements

    ( 1 - z ) ϕ 1 2 ( q , a q b q ; q , z ) = n = 0 ( a q , a z q / b ; q ) n ( b q , z q ; q ) n ( 1 - a z q 2 n + 1 ) ( b z ) n q n 2 , 1 𝑧 q-hypergeometric-rphis 2 1 𝑞 𝑎 𝑞 𝑏 𝑞 𝑞 𝑧 superscript subscript 𝑛 0 q-multiple-Pochhammer 𝑎 𝑞 𝑎 𝑧 𝑞 𝑏 𝑞 𝑛 q-multiple-Pochhammer 𝑏 𝑞 𝑧 𝑞 𝑞 𝑛 1 𝑎 𝑧 superscript 𝑞 2 𝑛 1 superscript 𝑏 𝑧 𝑛 superscript 𝑞 superscript 𝑛 2 {\displaystyle{\displaystyle(1-z){{}_{2}\phi_{1}}\left({q,aq\atop bq};q,z% \right)=\sum_{n=0}^{\infty}\frac{\left(aq,azq/b;q\right)_{n}}{\left(bq,zq;q% \right)_{n}}(1-azq^{2n+1})(bz)^{n}q^{n^{2}},}}
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    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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