DLMF:17.7.E11 (Q5407)

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DLMF:17.7.E11
No description defined

    Statements

    Defining formula
    ϕ 3 4 ⁡ ( q - n , q n + 1 , c , - c e , c 2 ⁢ q / e , - q ; q , q ) = ( e ⁢ q - n , e ⁢ q n + 1 , c 2 ⁢ q 1 - n / e , c 2 ⁢ q n + 2 / e ; q 2 ) ∞ ( e , c 2 ⁢ q / e ; q ) ∞ . q-hypergeometric-rphis 4 3 superscript 𝑞 𝑛 superscript 𝑞 𝑛 1 𝑐 𝑐 𝑒 superscript 𝑐 2 𝑞 𝑒 𝑞 𝑞 𝑞 q-multiple-Pochhammer 𝑒 superscript 𝑞 𝑛 𝑒 superscript 𝑞 𝑛 1 superscript 𝑐 2 superscript 𝑞 1 𝑛 𝑒 superscript 𝑐 2 superscript 𝑞 𝑛 2 𝑒 superscript 𝑞 2 q-multiple-Pochhammer 𝑒 superscript 𝑐 2 𝑞 𝑒 𝑞 {\displaystyle{\displaystyle{{}_{4}\phi_{3}}\left({q^{-n},q^{n+1},c,-c\atop e,% c^{2}q/e,-q};q,q\right)=\frac{\left(eq^{-n},eq^{n+1},c^{2}q^{1-n}/e,c^{2}q^{n+% 2}/e;q^{2}\right)_{\infty}}{\left(e,c^{2}q/e;q\right)_{\infty}}.}}
    0 references
    DLMF id
    DLMF:17.7.E11
    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.m2ajdec
    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.m6ajdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1jdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1cdec
    0 references
     
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