DLMF:17.7.E16 (Q5412): Difference between revisions

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DLMF:17.7.E16
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    Statements

    Defining formula
    ϕ 5 6 ⁡ ( a , q ⁢ a 1 2 , - q ⁢ a 1 2 , b , c , q - n a 1 2 , - a 1 2 , a ⁢ q / b , a ⁢ q / c , a ⁢ q n + 1 ; q , a ⁢ q n + 1 b ⁢ c ) = ( a ⁢ q , a ⁢ q / ( b ⁢ c ) ; q ) n ( a ⁢ q / b , a ⁢ q / c ; q ) n . q-hypergeometric-rphis 6 5 𝑎 𝑞 superscript 𝑎 1 2 𝑞 superscript 𝑎 1 2 𝑏 𝑐 superscript 𝑞 𝑛 superscript 𝑎 1 2 superscript 𝑎 1 2 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 superscript 𝑞 𝑛 1 𝑞 𝑎 superscript 𝑞 𝑛 1 𝑏 𝑐 q-multiple-Pochhammer 𝑎 𝑞 𝑎 𝑞 𝑏 𝑐 𝑞 𝑛 q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑞 𝑛 {\displaystyle{\displaystyle{{}_{6}\phi_{5}}\left({a,qa^{\frac{1}{2}},-qa^{% \frac{1}{2}},b,c,q^{-n}\atop a^{\frac{1}{2}},-a^{\frac{1}{2}},aq/b,aq/c,aq^{n+% 1}};q,\frac{aq^{n+1}}{bc}\right)=\frac{\left(aq,aq/(bc);q\right)_{n}}{\left(aq% /b,aq/c;q\right)_{n}}.}}
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    DLMF id
    DLMF:17.7.E16
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