DLMF:17.6.E9 (Q5376): 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 17:59, 30 December 2019

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DLMF:17.6.E9
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    ϕ 1 2 ( q , a q b q ; q , z ) = - ( 1 - b ) ( a q / b ) ( 1 - ( a q / b ) ) n = 0 ( a q , a z q / b ; q ) n q n ( a z q 2 / b ; q ) n + ( a q , a z q / b ; q ) ( a q / b ; q ) ϕ 1 2 ( q , 0 b q ; q , z ) , q-hypergeometric-rphis 2 1 𝑞 𝑎 𝑞 𝑏 𝑞 𝑞 𝑧 1 𝑏 𝑎 𝑞 𝑏 1 𝑎 𝑞 𝑏 superscript subscript 𝑛 0 q-multiple-Pochhammer 𝑎 𝑞 𝑎 𝑧 𝑞 𝑏 𝑞 𝑛 superscript 𝑞 𝑛 q-Pochhammer-symbol 𝑎 𝑧 superscript 𝑞 2 𝑏 𝑞 𝑛 q-multiple-Pochhammer 𝑎 𝑞 𝑎 𝑧 𝑞 𝑏 𝑞 q-Pochhammer-symbol 𝑎 𝑞 𝑏 𝑞 q-hypergeometric-rphis 2 1 𝑞 0 𝑏 𝑞 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({q,aq\atop bq};q,z\right)=-% \frac{(1-b)(aq/b)}{(1-(\ifrac{aq}{b}))}\sum_{n=0}^{\infty}\frac{\left(aq,azq/b% ;q\right)_{n}q^{n}}{\left(azq^{2}/b;q\right)_{n}}+\frac{\left(aq,azq/b;q\right% )_{\infty}}{\left(aq/b;q\right)_{\infty}}{{}_{2}\phi_{1}}\left({q,0\atop bq};q% ,z\right),}}
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    DLMF:17.6.E9
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    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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