DLMF:17.6.E4 (Q5371): Difference between revisions

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| c q | < | b 2 | 𝑐 𝑞 superscript 𝑏 2 {\displaystyle{\displaystyle|cq|<|b^{2}|}}

|cq|<|b^{2}|
Property / constraint: | c q | < | b 2 | 𝑐 𝑞 superscript 𝑏 2 {\displaystyle{\displaystyle|cq|<|b^{2}|}} / rank
 
Normal rank

Revision as of 17:58, 30 December 2019

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DLMF:17.6.E4
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    Statements

    ϕ 1 2 ( b 2 , b 2 / c c ; q 2 , c q / b 2 ) = 1 2 ( b 2 , q ; q 2 ) ( c , c q / b 2 ; q 2 ) ( ( c / b ; q ) ( b ; q ) + ( - c / b ; q ) ( - b ; q ) ) , q-hypergeometric-rphis 2 1 superscript 𝑏 2 superscript 𝑏 2 𝑐 𝑐 superscript 𝑞 2 𝑐 𝑞 superscript 𝑏 2 1 2 q-multiple-Pochhammer superscript 𝑏 2 𝑞 superscript 𝑞 2 q-multiple-Pochhammer 𝑐 𝑐 𝑞 superscript 𝑏 2 superscript 𝑞 2 q-Pochhammer-symbol 𝑐 𝑏 𝑞 q-Pochhammer-symbol 𝑏 𝑞 q-Pochhammer-symbol 𝑐 𝑏 𝑞 q-Pochhammer-symbol 𝑏 𝑞 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({b^{2},\ifrac{b^{2}}{c}\atop c% };q^{2},\ifrac{cq}{b^{2}}\right)=\frac{1}{2}\frac{\left(b^{2},q;q^{2}\right)_{% \infty}}{\left(c,cq/b^{2};q^{2}\right)_{\infty}}\left(\frac{\left(c/b;q\right)% _{\infty}}{\left(b;q\right)_{\infty}}+\frac{\left(-c/b;q\right)_{\infty}}{% \left(-b;q\right)_{\infty}}\right),}}
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    DLMF:17.6.E4
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    | c q | < | b 2 | 𝑐 𝑞 superscript 𝑏 2 {\displaystyle{\displaystyle|cq|<|b^{2}|}}
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