DLMF:17.2.E40 (Q5330)

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DLMF:17.2.E40
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    Statements

    Defining formula
    ∑ j = 0 2 ⁢ n ( - 1 ) j ⁢ [ 2 ⁢ n j ] q = ( q ; q 2 ) n . superscript subscript 𝑗 0 2 𝑛 superscript 1 𝑗 q-binomial 2 𝑛 𝑗 𝑞 q-Pochhammer-symbol 𝑞 superscript 𝑞 2 𝑛 {\displaystyle{\displaystyle\sum_{j=0}^{2n}(-1)^{j}\genfrac{[}{]}{0.0pt}{}{2n}% {j}_{q}=\left(q;q^{2}\right)_{n}.}}
    0 references
    DLMF id
    DLMF:17.2.E40
    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.m2aahdec
    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.m2akdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1aldec
    0 references
    Q11712
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C17.S1.XMD2.m1hdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1ajdec
    0 references
     
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