DLMF:17.7.E9 (Q5405)

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DLMF:17.7.E9
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    Statements

    Defining formula
    ϕ 3 4 ⁡ ( q - n , a ⁢ q n , c , - c ( a ⁢ q ) 1 2 , - ( a ⁢ q ) 1 2 , c 2 ; q , q ) = { 0 , n  odd, c n ⁢ ( q , a ⁢ q / c 2 ; q 2 ) n / 2 ( a ⁢ q , c 2 ⁢ q ; q 2 ) n / 2 , n  even. q-hypergeometric-rphis 4 3 superscript 𝑞 𝑛 𝑎 superscript 𝑞 𝑛 𝑐 𝑐 superscript 𝑎 𝑞 1 2 superscript 𝑎 𝑞 1 2 superscript 𝑐 2 𝑞 𝑞 cases 0 n  odd, superscript 𝑐 𝑛 q-multiple-Pochhammer 𝑞 𝑎 𝑞 superscript 𝑐 2 superscript 𝑞 2 𝑛 2 q-multiple-Pochhammer 𝑎 𝑞 superscript 𝑐 2 𝑞 superscript 𝑞 2 𝑛 2 n  even. {\displaystyle{\displaystyle{{}_{4}\phi_{3}}\left({q^{-n},aq^{n},c,-c\atop(aq)% ^{\frac{1}{2}},-(aq)^{\frac{1}{2}},c^{2}};q,q\right)=\begin{cases}0,&\mbox{$n$% odd,}\\ \dfrac{c^{n}\left(q,aq/c^{2};q^{2}\right)_{n/2}}{\left(aq,c^{2}q;q^{2}\right)_% {n/2}},&\mbox{$n$ even.}\end{cases}}}
    0 references
    DLMF id
    DLMF:17.7.E9
    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.m2ahdec
    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.m6ahdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1hdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1bdec
    0 references
     
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