DLMF:17.2.E33 (Q5323)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:17.2.E33
No description defined

    Statements

    Defining formula
    lim n → ∞ ⁡ [ n m ] q = 1 ( q ; q ) m = 1 ( 1 - q ) ⁢ ( 1 - q 2 ) ⁢ ⋯ ⁢ ( 1 - q m ) , subscript → 𝑛 q-binomial 𝑛 𝑚 𝑞 1 q-Pochhammer-symbol 𝑞 𝑞 𝑚 1 1 𝑞 1 superscript 𝑞 2 ⋯ 1 superscript 𝑞 𝑚 {\displaystyle{\displaystyle\lim_{n\to\infty}\genfrac{[}{]}{0.0pt}{}{n}{m}_{q}% =\frac{1}{\left(q;q\right)_{m}}=\frac{1}{(1-q)(1-q^{2})\cdots(1-q^{m})},}}
    0 references
    DLMF id
    DLMF:17.2.E33
    0 references
    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.m2aabdec
    0 references
    $$q$$ -binomial coefficient (or Gaussian polynomial)
    Defining formula
    [ n m ] q q-binomial 𝑛 𝑚 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar% {q}}}}
    xml-id
    C17.S2.E27.m2afdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1afdec
    0 references
    Q11716
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C17.S1.XMD3.m1fdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1acdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5323&oldid=51331"