DLMF:24.2.E8 (Q7407): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5acdec

Revision as of 01:24, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:24.2.E8
No description defined

    Statements

    Defining formula
    2 ⁢ e x ⁢ t e t + 1 = ∑ n = 0 ∞ E n ⁡ ( x ) ⁢ t n n ! , 2 superscript 𝑒 𝑥 𝑡 superscript 𝑒 𝑡 1 superscript subscript 𝑛 0 Euler-polynomial-E 𝑛 𝑥 superscript 𝑡 𝑛 𝑛 {\displaystyle{\displaystyle\frac{2e^{xt}}{e^{t}+1}=\sum_{n=0}^{\infty}E_{n}% \left(x\right)\frac{t^{n}}{n!},}}
    0 references
    DLMF id
    DLMF:24.2.E8
    0 references
    constraint
    | t | < π 𝑡 𝜋 {\displaystyle{\displaystyle|t|<\pi}}
    0 references
    Symbols used
    Q12114
    Defining formula
    E n ⁡ ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS2.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7407&oldid=31131"