DLMF:17.7.E2 (Q5398)

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DLMF:17.7.E2
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    Statements

    Defining formula
    ϕ 2 2 ⁡ ( a 2 , b 2 a ⁢ b ⁢ q 1 2 , - a ⁢ b ⁢ q 1 2 ; q , - q ) = ( a 2 ⁢ q , b 2 ⁢ q ; q 2 ) ∞ ( q , a 2 ⁢ b 2 ⁢ q ; q 2 ) ∞ . q-hypergeometric-rphis 2 2 superscript 𝑎 2 superscript 𝑏 2 𝑎 𝑏 superscript 𝑞 1 2 𝑎 𝑏 superscript 𝑞 1 2 𝑞 𝑞 q-multiple-Pochhammer superscript 𝑎 2 𝑞 superscript 𝑏 2 𝑞 superscript 𝑞 2 q-multiple-Pochhammer 𝑞 superscript 𝑎 2 superscript 𝑏 2 𝑞 superscript 𝑞 2 {\displaystyle{\displaystyle{{}_{2}\phi_{2}}\left({a^{2},b^{2}\atop abq^{\frac% {1}{2}},-abq^{\frac{1}{2}}};q,-q\right)=\frac{\left(a^{2}q,b^{2}q;q^{2}\right)% _{\infty}}{\left(q,a^{2}b^{2}q;q^{2}\right)_{\infty}}.}}
    0 references
    DLMF id
    DLMF:17.7.E2
    0 references
    Symbols used
    basic hypergeometric (or $$q$$ -hypergeometric) function
    Defining formula
    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.m2aadec
    0 references
    Q11713
    Defining formula
    ( 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.m6aadec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1adec
    0 references
     
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