DLMF:17.2.E45 (Q5335)

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DLMF:17.2.E45
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    Statements

    Defining formula
    ∫ 0 1 f ⁢ ( x ) ⁢ d q x = ( 1 - q ) ⁢ ∑ j = 0 ∞ f ⁢ ( q j ) ⁢ q j , superscript subscript 0 1 𝑓 𝑥 q-differential 𝑞 𝑥 1 𝑞 superscript subscript 𝑗 0 𝑓 superscript 𝑞 𝑗 superscript 𝑞 𝑗 {\displaystyle{\displaystyle\int_{0}^{1}f(x){\mathrm{d}}_{q}x=(1-q)\sum_{j=0}^% {\infty}f(q^{j})q^{j},}}
    0 references
    DLMF id
    DLMF:17.2.E45
    0 references
    Symbols used
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11299
    Defining formula
    d q x q-differential 𝑞 𝑥 {\displaystyle{\displaystyle{\mathrm{d}}_{\NVar{q}}\NVar{x}}}
    xml-id
    C17.S2.SS5.p1.m3adec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1aqdec
    0 references
    Q11712
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C17.S1.XMD2.m1kdec
    0 references
    Q11719
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C17.S1.XMD8.m1dec
    0 references
     
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