DLMF:4.13.E10 (Q1651): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aadec

Revision as of 18:17, 1 January 2020

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DLMF:4.13.E10
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    Statements

    Defining formula
    Wp ⁡ ( x ) = ξ - ln ⁡ ξ + ln ⁡ ξ ξ + ( ln ⁡ ξ ) 2 2 ⁢ ξ 2 - ln ⁡ ξ ξ 2 + O ⁡ ( ( ln ⁡ ξ ) 3 ξ 3 ) , Lambert-Wp 𝑥 𝜉 𝜉 𝜉 𝜉 superscript 𝜉 2 2 superscript 𝜉 2 𝜉 superscript 𝜉 2 Big-O superscript 𝜉 3 superscript 𝜉 3 {\displaystyle{\displaystyle\mathrm{Wp}\left(x\right)=\xi-\ln\xi+\frac{\ln\xi}% {\xi}+\frac{(\ln\xi)^{2}}{2\xi^{2}}-\frac{\ln\xi}{\xi^{2}}+O\left(\frac{(\ln% \xi)^{3}}{\xi^{3}}\right),}}
    0 references
    DLMF id
    DLMF:4.13.E10
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    Q11233
    Defining formula
    Wp ⁡ ( x ) Lambert-Wp 𝑥 {\displaystyle{\displaystyle\mathrm{Wp}\left(\NVar{x}\right)}}
    xml-id
    C4.S13.p2.m8acdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
     
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