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DLMF:17.8.E4 - MaRDI portal

DLMF:17.8.E4 (Q6120)

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DLMF:17.8.E4
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    Statements

    DLMF defining formula
    ψ 2 2 ⁡ ( b , c ; a ⁢ q / b , a ⁢ q / c ; q , - a ⁢ q / ( b ⁢ c ) ) = ( a ⁢ q / ( b ⁢ c ) ; q ) ∞ ⁢ ( a ⁢ q 2 / b 2 , a ⁢ q 2 / c 2 , q 2 , a ⁢ q , q / a ; q 2 ) ∞ ( a ⁢ q / b , a ⁢ q / c , q / b , q / c , - a ⁢ q / ( b ⁢ c ) ; q ) ∞ , q-hypergeometric-rpsis 2 2 𝑏 𝑐 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑞 𝑎 𝑞 𝑏 𝑐 q-Pochhammer-symbol 𝑎 𝑞 𝑏 𝑐 𝑞 q-multiple-Pochhammer 𝑎 superscript 𝑞 2 superscript 𝑏 2 𝑎 superscript 𝑞 2 superscript 𝑐 2 superscript 𝑞 2 𝑎 𝑞 𝑞 𝑎 superscript 𝑞 2 q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑞 𝑏 𝑞 𝑐 𝑎 𝑞 𝑏 𝑐 𝑞 {\displaystyle{\displaystyle{{}_{2}\psi_{2}}\left(b,c;aq/b,aq/c;q,-aq/(bc)% \right)=\frac{\left(aq/(bc);q\right)_{\infty}\left(aq^{2}/b^{2},aq^{2}/c^{2},q% ^{2},aq,q/a;q^{2}\right)_{\infty}}{\left(aq/b,aq/c,q/b,q/c,-aq/(bc);q\right)_{% \infty}},}}
    0 references
    Symbols used
    Q11269
    DLMF defining formula
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2adec
    0 references
    bilateral basic hypergeometric (or bilateral $$q$$ -hypergeometric) function
    DLMF defining formula
    ψ s r ⁡ ( a 1 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rpsis 𝑟 𝑠 subscript 𝑎 1 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r}}\psi_{\NVar{s}}}\left(\NVar{a_{1},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
    xml-id
    C17.S4.E3.m2aadec
    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.m6acdec
    0 references
    complex base
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1cdec
    0 references

    Identifiers

     
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