DLMF:2.1.E12 (Q697): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10926 / rank
 
Normal rank
Property / Symbols used: Q10926 / qualifier
 
Defining formula:

f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}

f(x)
Property / Symbols used: Q10926 / qualifier
 
xml-id: C2.S1.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: Q10927 / rank
 
Normal rank
Property / Symbols used: Q10927 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q10927 / qualifier
 
xml-id: C2.S1.XMD7.m1adec

Latest revision as of 16:47, 1 January 2020

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DLMF:2.1.E12
No description defined

    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
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
    Q10926
    Defining formula
    f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    xml-id
    C2.S1.XMD6.m1adec
    0 references
    Q10927
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C2.S1.XMD7.m1adec
    0 references
     
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