DLMF:24.4.E26 (Q7439)

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DLMF:24.4.E26
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    Statements

    Defining formula
    E n ⁡ ( 0 ) = - E n ⁡ ( 1 ) = - 2 n + 1 ⁢ ( 2 n + 1 - 1 ) ⁢ B n + 1 , Euler-polynomial-E 𝑛 0 Euler-polynomial-E 𝑛 1 2 𝑛 1 superscript 2 𝑛 1 1 Bernoulli-number-B 𝑛 1 {\displaystyle{\displaystyle E_{n}\left(0\right)=-E_{n}\left(1\right)=-\frac{2% }{n+1}(2^{n+1}-1)B_{n+1},}}
    0 references
    DLMF id
    DLMF:24.4.E26
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    constraint
    n > 0 𝑛 0 {\displaystyle{\displaystyle n>0}}
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    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1agdec
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    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.m2akdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1ydec
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