DLMF:17.7.E16 (Q5412)

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DLMF:17.7.E16
No description defined

    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}}.}}
    0 references
    DLMF id
    DLMF:17.7.E16
    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.m2aodec
    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.m6aodec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1odec
    0 references
     
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