DLMF:17.9.E15 (Q5441)

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DLMF:17.9.E15
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    Statements

    Defining formula
    ( a ⁢ q , a ⁢ q / ( d ⁢ e ) ; q ) n ( a ⁢ q / d , a ⁢ q / e ; q ) n ⁢ ϕ 3 4 ⁡ ( a ⁢ q / ( b ⁢ c ) , d , e , q - n a ⁢ q / b , a ⁢ q / c , d ⁢ e ⁢ q - n / a ; q , q ) = ϕ 7 8 ⁡ ( a , q ⁢ a 1 2 , - q ⁢ a 1 2 , b , c , d , e , q - n a 1 2 , - a 1 2 , a ⁢ q / b , a ⁢ q / c , a ⁢ q / d , a ⁢ q / e , a ⁢ q n + 1 ; q , a 2 ⁢ q 2 + n b ⁢ c ⁢ d ⁢ e ) . q-multiple-Pochhammer 𝑎 𝑞 𝑎 𝑞 𝑑 𝑒 𝑞 𝑛 q-multiple-Pochhammer 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑞 𝑛 q-hypergeometric-rphis 4 3 𝑎 𝑞 𝑏 𝑐 𝑑 𝑒 superscript 𝑞 𝑛 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑑 𝑒 superscript 𝑞 𝑛 𝑎 𝑞 𝑞 q-hypergeometric-rphis 8 7 𝑎 𝑞 superscript 𝑎 1 2 𝑞 superscript 𝑎 1 2 𝑏 𝑐 𝑑 𝑒 superscript 𝑞 𝑛 superscript 𝑎 1 2 superscript 𝑎 1 2 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑒 𝑎 superscript 𝑞 𝑛 1 𝑞 superscript 𝑎 2 superscript 𝑞 2 𝑛 𝑏 𝑐 𝑑 𝑒 {\displaystyle{\displaystyle\frac{\left(aq,aq/(de);q\right)_{n}}{\left(aq/d,aq% /e;q\right)_{n}}{{}_{4}\phi_{3}}\left({aq/(bc),d,e,q^{-n}\atop aq/b,aq/c,deq^{% -n}/a};q,q\right)={{}_{8}\phi_{7}}\left({a,qa^{\frac{1}{2}},-qa^{\frac{1}{2}},% b,c,d,e,q^{-n}\atop a^{\frac{1}{2}},-a^{\frac{1}{2}},aq/b,aq/c,aq/d,aq/e,aq^{n% +1}};q,\frac{a^{2}q^{2+n}}{bcde}\right).}}
    0 references
    DLMF id
    DLMF:17.9.E15
    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.m2andec
    0 references
     
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