DLMF:24.14.E6 (Q7551)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:24.14.E6
No description defined

    Statements

    Defining formula
    ∑ k = 0 n ( n k ) ⁢ 2 k ⁢ B k ⁢ E n - k = 2 ⁢ ( 1 - 2 n - 1 ) ⁢ B n - n ⁢ E n - 1 . superscript subscript 𝑘 0 𝑛 binomial 𝑛 𝑘 superscript 2 𝑘 Bernoulli-number-B 𝑘 Euler-number-E 𝑛 𝑘 2 1 superscript 2 𝑛 1 Bernoulli-number-B 𝑛 𝑛 Euler-number-E 𝑛 1 {\displaystyle{\displaystyle\sum_{k=0}^{n}{n\choose k}2^{k}B_{k}E_{n-k}=2(1-2^% {n-1})B_{n}-nE_{n-1}.}}
    0 references
    DLMF id
    DLMF:24.14.E6
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1abdec
    0 references
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1aadec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aedec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1edec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1edec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7551&oldid=34457"