DLMF:2.1.E12 (Q697)

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DLMF:2.1.E12
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    Statements

    Defining formula
    ∫ f ⁢ ( x ) ⁢ d x ∼ { a constant, ℜ ⁡ ν < - 1 , ln ⁡ x , ν = - 1 , x ν + 1 / ( ν + 1 ) , ℜ ⁡ ν > - 1 . asymptotically-equals 𝑓 𝑥 𝑥 cases a constant, 𝜈 1 𝑥 𝜈 1 superscript 𝑥 𝜈 1 𝜈 1 𝜈 1 {\displaystyle{\displaystyle\int f(x)\mathrm{d}x\sim\begin{cases}\text{a % constant,}&\Re\nu<-1,\\ \ln x,&\phantom{\Re missing}\nu=-1,\\ x^{\nu+1}/(\nu+1),&\Re\nu>-1.\end{cases}}}
    0 references
    DLMF id
    DLMF:2.1.E12
    0 references
    Symbols used
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2acdec
    0 references
     
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