DLMF:24.4.E8 (Q7421)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:24.4.E8
No description defined

    Statements

    Defining formula
    ∑ k = 1 m ( - 1 ) m - k ⁢ k n = E n ⁡ ( m + 1 ) + ( - 1 ) m ⁢ E n ⁡ ( 0 ) 2 . superscript subscript 𝑘 1 𝑚 superscript 1 𝑚 𝑘 superscript 𝑘 𝑛 Euler-polynomial-E 𝑛 𝑚 1 superscript 1 𝑚 Euler-polynomial-E 𝑛 0 2 {\displaystyle{\displaystyle\sum_{k=1}^{m}(-1)^{m-k}k^{n}=\frac{E_{n}\left(m+1% \right)+(-1)^{m}E_{n}\left(0\right)}{2}.}}
    0 references
    DLMF id
    DLMF:24.4.E8
    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.m2acdec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1adec
    0 references
    Q12115
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C24.S1.XMD4.m1adec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1gdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7421&oldid=31335"