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DLMF:17.2.E46 - MaRDI portal

DLMF:17.2.E46 (Q6033)

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DLMF:17.2.E46
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    Statements

    DLMF defining formula
    ∫ 0 a f ⁢ ( x ) ⁢ d q x = a ⁢ ( 1 - q ) ⁢ ∑ j = 0 ∞ f ⁢ ( a ⁢ q j ) ⁢ q j . superscript subscript 0 𝑎 𝑓 𝑥 q-differential 𝑞 𝑥 𝑎 1 𝑞 superscript subscript 𝑗 0 𝑓 𝑎 superscript 𝑞 𝑗 superscript 𝑞 𝑗 {\displaystyle{\displaystyle\int_{0}^{a}f(x){\mathrm{d}}_{q}x=a(1-q)\sum_{j=0}% ^{\infty}f(aq^{j})q^{j}.}}
    0 references
    Symbols used
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q11270
    DLMF defining formula
    d q x q-differential 𝑞 𝑥 {\displaystyle{\displaystyle{\mathrm{d}}_{\NVar{q}}\NVar{x}}}
    xml-id
    C17.S2.SS5.p1.m3aadec
    0 references
    complex base
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1ardec
    0 references
    nonnegative integer
    DLMF defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C17.S1.XMD2.m1ldec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C17.S1.XMD8.m1adec
    0 references

    Identifiers

     
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