DLMF:17.9.E18 (Q5444)

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DLMF:17.9.E18
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    Statements

    test
    ( ϕ 3 4 ⁡ ( a , b , a ⁢ b ⁢ z , a ⁢ b / z a ⁢ b ⁢ q 1 2 , - a ⁢ b ⁢ q 1 2 , - a ⁢ b ; q , q ) ) 2 = ϕ 4 5 ⁡ ( a 2 , b 2 , a ⁢ b , a ⁢ b ⁢ z , a ⁢ b / z a ⁢ b ⁢ q 1 2 , - a ⁢ b ⁢ q 1 2 , - a ⁢ b , a 2 ⁢ b 2 ; q , q ) , superscript q-hypergeometric-rphis 4 3 𝑎 𝑏 𝑎 𝑏 𝑧 𝑎 𝑏 𝑧 𝑎 𝑏 superscript 𝑞 1 2 𝑎 𝑏 superscript 𝑞 1 2 𝑎 𝑏 𝑞 𝑞 2 q-hypergeometric-rphis 5 4 superscript 𝑎 2 superscript 𝑏 2 𝑎 𝑏 𝑎 𝑏 𝑧 𝑎 𝑏 𝑧 𝑎 𝑏 superscript 𝑞 1 2 𝑎 𝑏 superscript 𝑞 1 2 𝑎 𝑏 superscript 𝑎 2 superscript 𝑏 2 𝑞 𝑞 {\displaystyle{\displaystyle\left({{}_{4}\phi_{3}}\left({a,b,abz,ab/z\atop abq% ^{\frac{1}{2}},-abq^{\frac{1}{2}},-ab};q,q\right)\right)^{2}={{}_{5}\phi_{4}}% \left({a^{2},b^{2},ab,abz,ab/z\atop abq^{\frac{1}{2}},-abq^{\frac{1}{2}},-ab,a% ^{2}b^{2}};q,q\right),}}
    0 references
    DLMF id
    DLMF:17.9.E18
    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.m2aqdec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1qdec
    0 references
    Q11718
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1fdec
    0 references
     
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