DLMF:4.13.E11 (Q1652): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
test:

O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11236 / rank
 
Normal rank
Property / Symbols used: Q11236 / qualifier
 
test:

Wm ⁡ ( x ) Lambert-Wm 𝑥 {\displaystyle{\displaystyle\mathrm{Wm}\left(\NVar{x}\right)}}

\LambertWm@{\NVar{x}}
Property / Symbols used: Q11236 / qualifier
 
xml-id: C4.S13.p2.m10abdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11237 / rank
 
Normal rank
Property / Symbols used: Q11237 / qualifier
 
test:

η 𝜂 {\displaystyle{\displaystyle\eta}}

\eta
Property / Symbols used: Q11237 / qualifier
 
xml-id: C4.S13.XMD3.m1dec

Latest revision as of 17:18, 1 January 2020

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DLMF:4.13.E11
No description defined

    Statements

    test
    Wm ⁡ ( x ) = - η - ln ⁡ η - ln ⁡ η η - ( ln ⁡ η ) 2 2 ⁢ η 2 - ln ⁡ η η 2 + O ⁡ ( ( ln ⁡ η ) 3 η 3 ) , Lambert-Wm 𝑥 𝜂 𝜂 𝜂 𝜂 superscript 𝜂 2 2 superscript 𝜂 2 𝜂 superscript 𝜂 2 Big-O superscript 𝜂 3 superscript 𝜂 3 {\displaystyle{\displaystyle\mathrm{Wm}\left(x\right)=-\eta-\ln\eta-\frac{\ln% \eta}{\eta}-\frac{(\ln\eta)^{2}}{2\eta^{2}}-\frac{\ln\eta}{\eta^{2}}+O\left(% \frac{(\ln\eta)^{3}}{\eta^{3}}\right),}}
    0 references
    DLMF id
    DLMF:4.13.E11
    0 references
    Symbols used
    order not exceeding
    test
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    Q11236
    test
    Wm ⁡ ( x ) Lambert-Wm 𝑥 {\displaystyle{\displaystyle\mathrm{Wm}\left(\NVar{x}\right)}}
    xml-id
    C4.S13.p2.m10abdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
    Q11218
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1fdec
    0 references
    Q11237
    test
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C4.S13.XMD3.m1dec
    0 references
     
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