DLMF:4.13.E6 (Q1647): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2afdec

Revision as of 18:17, 1 January 2020

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DLMF:4.13.E6
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    Statements

    Defining formula
    W ⁡ ( - e - 1 - ( t 2 / 2 ) ) = ∑ n = 0 ∞ ( - 1 ) n - 1 ⁢ c n ⁢ t n , Lambert-W superscript 𝑒 1 superscript 𝑡 2 2 superscript subscript 𝑛 0 superscript 1 𝑛 1 subscript 𝑐 𝑛 superscript 𝑡 𝑛 {\displaystyle{\displaystyle W\left(-e^{-1-(t^{2}/2)}\right)=\sum_{n=0}^{% \infty}(-1)^{n-1}c_{n}t^{n},}}
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    DLMF id
    DLMF:4.13.E6
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    constraint
    | t | < 2 ⁢ π 𝑡 2 𝜋 {\displaystyle{\displaystyle|t|<2\sqrt{\pi}}}
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    Symbols used
    Lambert $$W$$ -function
    Defining formula
    W ⁡ ( x ) Lambert-W 𝑥 {\displaystyle{\displaystyle W\left(\NVar{x}\right)}}
    xml-id
    C4.S13.E1.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
     
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