DLMF:17.5.E4 (Q5366)

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DLMF:17.5.E4
No description defined

    Statements

    Defining formula
    ϕ 0 1 ⁡ ( 0 ; - ; q , z ) = ∑ n = 0 ∞ z n ( q ; q ) n = 1 ( z ; q ) ∞ , q-hypergeometric-rphis 1 0 0 𝑞 𝑧 superscript subscript 𝑛 0 superscript 𝑧 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑛 1 q-Pochhammer-symbol 𝑧 𝑞 {\displaystyle{\displaystyle{{}_{1}\phi_{0}}\left(0;-;q,z\right)=\sum_{n=0}^{% \infty}\frac{z^{n}}{\left(q;q\right)_{n}}=\frac{1}{\left(z;q\right)_{\infty}},}}
    0 references
    DLMF id
    DLMF:17.5.E4
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    Symbols used
    Q11298
    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.m2acdec
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    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.m2acdec
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    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1cdec
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    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1bdec
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    Q11718
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1cdec
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