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2.1.E11 - MaRDI portal

2.1.E11 (Q666)

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2.1.E11
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    Statements

    DLMF defining formula
    ∫ x ∞ f ⁢ ( t ) ⁢ d t ∼ - x ν + 1 ν + 1 , asymptotically-equals superscript subscript 𝑥 𝑓 𝑡 𝑡 superscript 𝑥 𝜈 1 𝜈 1 {\displaystyle{\displaystyle\int_{x}^{\infty}f(t)\mathrm{d}t\sim-\frac{x^{\nu+% 1}}{\nu+1},}}
    0 references
    constraint
    ℜ ⁡ ν < - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu<-1}}
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    Symbols used
    asymptotic equality
    DLMF defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2abdec
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    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.m3adec
    0 references
    real part
    DLMF defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    continuous function
    DLMF defining formula
    f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    xml-id
    C2.S1.XMD6.m1dec
    0 references
    complex constant
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C2.S1.XMD7.m1dec
    0 references

    Identifiers

     
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