DLMF:17.9.E17 (Q5443)

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DLMF:17.9.E17
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    Statements

    Defining formula
    ϕ 2 3 ⁡ ( a , b , c a ⁢ q / b , a ⁢ q / c ; q , a ⁢ q ⁢ z b ⁢ c ) = ( a ⁢ z ; q ) ∞ ( z ; q ) ∞ ⁢ ϕ 4 5 ⁡ ( a 1 2 , - a 1 2 , ( a ⁢ q ) 1 2 , - ( a ⁢ q ) 1 2 , a ⁢ q / ( b ⁢ c ) a ⁢ q / b , a ⁢ q / c , a ⁢ z , q / z ; q , q ) . q-hypergeometric-rphis 3 2 𝑎 𝑏 𝑐 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑞 𝑎 𝑞 𝑧 𝑏 𝑐 q-Pochhammer-symbol 𝑎 𝑧 𝑞 q-Pochhammer-symbol 𝑧 𝑞 q-hypergeometric-rphis 5 4 superscript 𝑎 1 2 superscript 𝑎 1 2 superscript 𝑎 𝑞 1 2 superscript 𝑎 𝑞 1 2 𝑎 𝑞 𝑏 𝑐 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑧 𝑞 𝑧 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({a,b,c\atop aq/b,aq/c};q,% \frac{aqz}{bc}\right)=\frac{\left(az;q\right)_{\infty}}{\left(z;q\right)_{% \infty}}\*{{}_{5}\phi_{4}}\left({a^{\frac{1}{2}},-a^{\frac{1}{2}},(aq)^{\frac{% 1}{2}},-(aq)^{\frac{1}{2}},aq/(bc)\atop aq/b,aq/c,az,q/z};q,q\right).}}
    0 references
    DLMF id
    DLMF:17.9.E17
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    Symbols used
    Q11298
    Defining formula
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2ahdec
    0 references
    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.m2apdec
    0 references
     
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