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DLMF:17.7.E14 - MaRDI portal

DLMF:17.7.E14 (Q6107)

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DLMF:17.7.E14
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    Statements

    DLMF defining formula
    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 , q ) = ( a ⁢ q , a ⁢ q / ( b ⁢ c ) , a ⁢ q / ( b ⁢ d ) , a ⁢ q / ( c ⁢ d ) ; q ) n ( a ⁢ q / b , a ⁢ q / c , a ⁢ q / d , a ⁢ q / ( b ⁢ c ⁢ d ) ; q ) n , 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 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑎 𝑞 𝑏 𝑐 𝑎 𝑞 𝑏 𝑑 𝑎 𝑞 𝑐 𝑑 𝑞 𝑛 q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑎 𝑞 𝑏 𝑐 𝑑 𝑞 𝑛 {\displaystyle{\displaystyle{{}_{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,q\right)=\frac{\left(aq,aq/(bc),aq/(bd),aq/(cd);q\right)_{% n}}{\left(aq/b,aq/c,aq/d,aq/(bcd);q\right)_{n}},}}
    0 references
    Symbols used
    basic hypergeometric (or $$q$$ -hypergeometric) function
    DLMF 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.m2amdec
    0 references
    Q11684
    DLMF 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.m6amdec
    0 references
    complex base
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1mdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1fdec
    0 references

    Identifiers

     
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