DLMF:24.5.E1 (Q7453)

From DRMF
Revision as of 01:29, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:24.5.E1
No description defined

    Statements

    Defining formula
    ∑ k = 0 n - 1 ( n k ) ⁢ B k ⁡ ( x ) = n ⁢ x n - 1 , superscript subscript 𝑘 0 𝑛 1 binomial 𝑛 𝑘 Bernoulli-polynomial-B 𝑘 𝑥 𝑛 superscript 𝑥 𝑛 1 {\displaystyle{\displaystyle\sum_{k=0}^{n-1}{n\choose k}B_{k}\left(x\right)=nx% ^{n-1},}}
    0 references
    DLMF id
    DLMF:24.5.E1
    0 references
    constraint
    n = 2 , 3 , … 𝑛 2 3 … {\displaystyle{\displaystyle n=2,3,\dots}}
    0 references
    Symbols used
    Q11288
    Defining formula
    B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS1.m2adec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1dec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1dec
    0 references
    Q12112
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C24.S1.XMD7.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7453&oldid=31981"