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

From DRMF
Jump to navigation Jump to search
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
(5 intermediate revisions by the same user not shown)
Property / constraint
 

| t | < 2 ⁢ π 𝑡 2 𝜋 {\displaystyle{\displaystyle|t|<2\sqrt{\pi}}}

|t|<2\sqrt{\pi}
Property / constraint: | t | < 2 ⁢ π 𝑡 2 𝜋 {\displaystyle{\displaystyle|t|<2\sqrt{\pi}}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Lambert $$W$$ -function / rank
 
Normal rank
Property / Symbols used: Lambert $$W$$ -function / qualifier
 
Defining formula:

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

\LambertW@{\NVar{x}}
Property / Symbols used: Lambert $$W$$ -function / qualifier
 
xml-id: C4.S13.E1.m2addec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2adec
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
Property / Symbols used
 
Property / Symbols used: Q11223 / rank
 
Normal rank
Property / Symbols used: Q11223 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11223 / qualifier
 
xml-id: C4.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11234 / rank
 
Normal rank
Property / Symbols used: Q11234 / qualifier
 
Defining formula:

c i subscript 𝑐 𝑖 {\displaystyle{\displaystyle c_{i}}}

c_{i}
Property / Symbols used: Q11234 / qualifier
 
xml-id: C4.S13.XMD1.m1dec

Latest revision as of 18:17, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:4.13.E6
No description defined

    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},}}
    0 references
    DLMF id
    DLMF:4.13.E6
    0 references
    constraint
    | t | < 2 ⁢ π 𝑡 2 𝜋 {\displaystyle{\displaystyle|t|<2\sqrt{\pi}}}
    0 references
    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
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1adec
    0 references
    Q11234
    Defining formula
    c i subscript 𝑐 𝑖 {\displaystyle{\displaystyle c_{i}}}
    xml-id
    C4.S13.XMD1.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q1647&oldid=27000"