DLMF:17.6.E8 (Q5375): Difference between revisions

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Property / constraint
 

| z | < 1 , | a b z | < | c | formulae-sequence 𝑧 1 𝑎 𝑏 𝑧 𝑐 {\displaystyle{\displaystyle|z|<1,|abz|<|c|}}

|z|<1,|abz|<|c|
Property / constraint: | z | < 1 , | a b z | < | c | formulae-sequence 𝑧 1 𝑎 𝑏 𝑧 𝑐 {\displaystyle{\displaystyle|z|<1,|abz|<|c|}} / rank
 
Normal rank

Revision as of 16:59, 30 December 2019

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DLMF:17.6.E8
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    Statements

    ϕ 1 2 ( a , b c ; q , z ) = ( a b z / c ; q ) ( z ; q ) ϕ 1 2 ( c / a , c / b c ; q , a b z / c ) , q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 q-Pochhammer-symbol 𝑎 𝑏 𝑧 𝑐 𝑞 q-Pochhammer-symbol 𝑧 𝑞 q-hypergeometric-rphis 2 1 𝑐 𝑎 𝑐 𝑏 𝑐 𝑞 𝑎 𝑏 𝑧 𝑐 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=% \frac{\left(\ifrac{abz}{c};q\right)_{\infty}}{\left(z;q\right)_{\infty}}{{}_{2% }\phi_{1}}\left({c/a,c/b\atop c};q,\ifrac{abz}{c}\right),}}
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    | z | < 1 , | a b z | < | c | formulae-sequence 𝑧 1 𝑎 𝑏 𝑧 𝑐 {\displaystyle{\displaystyle|z|<1,|abz|<|c|}}
    0 references