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DLMF:17.7.E8 - MaRDI portal

DLMF:17.7.E8 (Q6101)

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DLMF:17.7.E8
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    Statements

    DLMF defining formula
    ϕ 7 8 ⁡ ( λ , q ⁢ λ 1 2 , - q ⁢ λ 1 2 , a , b , c , - c , λ ⁢ q / c 2 λ 1 2 , - λ 1 2 , λ ⁢ q / a , λ ⁢ q / b , λ ⁢ q / c , - λ ⁢ q / c , c 2 ; q , - λ ⁢ q a ⁢ b ) = ( λ ⁢ q , c 2 / λ ; q ) ∞ ⁢ ( a ⁢ q , b ⁢ q , c 2 ⁢ q / a , c 2 ⁢ q / b ; q 2 ) ∞ ( λ ⁢ q / a , λ ⁢ q / b ; q ) ∞ ⁢ ( q , a ⁢ b ⁢ q , c 2 ⁢ q , c 2 ⁢ q / ( a ⁢ b ) ; q 2 ) ∞ , q-hypergeometric-rphis 8 7 𝜆 𝑞 superscript 𝜆 1 2 𝑞 superscript 𝜆 1 2 𝑎 𝑏 𝑐 𝑐 𝜆 𝑞 superscript 𝑐 2 superscript 𝜆 1 2 superscript 𝜆 1 2 𝜆 𝑞 𝑎 𝜆 𝑞 𝑏 𝜆 𝑞 𝑐 𝜆 𝑞 𝑐 superscript 𝑐 2 𝑞 𝜆 𝑞 𝑎 𝑏 q-multiple-Pochhammer 𝜆 𝑞 superscript 𝑐 2 𝜆 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑞 superscript 𝑐 2 𝑞 𝑎 superscript 𝑐 2 𝑞 𝑏 superscript 𝑞 2 q-multiple-Pochhammer 𝜆 𝑞 𝑎 𝜆 𝑞 𝑏 𝑞 q-multiple-Pochhammer 𝑞 𝑎 𝑏 𝑞 superscript 𝑐 2 𝑞 superscript 𝑐 2 𝑞 𝑎 𝑏 superscript 𝑞 2 {\displaystyle{\displaystyle{{}_{8}\phi_{7}}\left({\lambda,q\lambda^{\frac{1}{% 2}},-q\lambda^{\frac{1}{2}},a,b,c,-c,\lambda q/c^{2}\atop\lambda^{\frac{1}{2}}% ,-\lambda^{\frac{1}{2}},\lambda q/a,\lambda q/b,\lambda q/c,-\lambda q/c,c^{2}% };q,-\frac{\lambda q}{ab}\right)=\frac{\left(\lambda q,c^{2}/\lambda;q\right)_% {\infty}\left(aq,bq,c^{2}q/a,c^{2}q/b;q^{2}\right)_{\infty}}{\left(\lambda q/a% ,\lambda q/b;q\right)_{\infty}\left(q,abq,c^{2}q,c^{2}q/(ab);q^{2}\right)_{% \infty}},}}
    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.m2agdec
    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.m6agdec
    0 references
    complex base
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1gdec
    0 references

    Identifiers

     
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