DLMF:17.2.E39 (Q5329)

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DLMF:17.2.E39
No description defined

    Statements

    Defining formula
    ∑ j = 0 n [ n j ] q 2 ⁢ q j = ( - q ; q ) n , superscript subscript 𝑗 0 𝑛 q-binomial 𝑛 𝑗 superscript 𝑞 2 superscript 𝑞 𝑗 q-Pochhammer-symbol 𝑞 𝑞 𝑛 {\displaystyle{\displaystyle\sum_{j=0}^{n}\genfrac{[}{]}{0.0pt}{}{n}{j}_{q^{2}% }q^{j}=\left(-q;q\right)_{n},}}
    0 references
    DLMF id
    DLMF:17.2.E39
    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.m2aagdec
    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.m2ajdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1akdec
    0 references
    Q11712
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C17.S1.XMD2.m1gdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1aidec
    0 references
     
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