DLMF:17.7.E12 (Q5408)

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DLMF:17.7.E12
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    Statements

    test
    ϕ 3 4 ⁡ ( a , a ⁢ q , b 2 ⁢ q 2 ⁢ n , q - 2 ⁢ n b , b ⁢ q , a 2 ⁢ q 2 ; q 2 , q 2 ) = a n ⁢ ( - q , b / a ; q ) n ( - a ⁢ q , b ; q ) n . q-hypergeometric-rphis 4 3 𝑎 𝑎 𝑞 superscript 𝑏 2 superscript 𝑞 2 𝑛 superscript 𝑞 2 𝑛 𝑏 𝑏 𝑞 superscript 𝑎 2 superscript 𝑞 2 superscript 𝑞 2 superscript 𝑞 2 superscript 𝑎 𝑛 q-multiple-Pochhammer 𝑞 𝑏 𝑎 𝑞 𝑛 q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑞 𝑛 {\displaystyle{\displaystyle{{}_{4}\phi_{3}}\left({a,aq,b^{2}q^{2n},q^{-2n}% \atop b,bq,a^{2}q^{2}};q^{2},q^{2}\right)=\frac{a^{n}\left(-q,b/a;q\right)_{n}% }{\left(-aq,b;q\right)_{n}}.}}
    0 references
    DLMF id
    DLMF:17.7.E12
    0 references
    Symbols used
    basic hypergeometric (or $$q$$ -hypergeometric) function
    test
    ϕ s r + 1 ⁡ ( a 0 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rphis 𝑟 1 𝑠 subscript 𝑎 0 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
    xml-id
    C17.S4.E1.m2akdec
    0 references
    Q11713
    test
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6akdec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1kdec
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    Q11711
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1ddec
    0 references
     
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