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DLMF:17.2.E47 - MaRDI portal

DLMF:17.2.E47 (Q6034)

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DLMF:17.2.E47
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    Statements

    DLMF defining formula
    lim q → 1 - ⁡ ∫ 0 a f ⁢ ( x ) ⁢ d q x = ∫ 0 a f ⁢ ( x ) ⁢ d x . subscript → 𝑞 limit-from 1 superscript subscript 0 𝑎 𝑓 𝑥 q-differential 𝑞 𝑥 superscript subscript 0 𝑎 𝑓 𝑥 𝑥 {\displaystyle{\displaystyle\lim_{q\to 1-}\int_{0}^{a}f(x){\mathrm{d}}_{q}x=% \int_{0}^{a}f(x)\mathrm{d}x.}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    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.m3abdec
    0 references
    complex base
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1asdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C17.S1.XMD8.m1bdec
    0 references

    Identifiers

     
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