DLMF:24.13.E11 (Q7545)

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DLMF:24.13.E11
No description defined

    Statements

    Defining formula
    ∫ 0 1 E n ⁡ ( t ) ⁢ E m ⁡ ( t ) ⁢ d t = ( - 1 ) n ⁢ 4 ⁢ ( 2 m + n + 2 - 1 ) ⁢ m ! ⁢ n ! ( m + n + 2 ) ! ⁢ B m + n + 2 . superscript subscript 0 1 Euler-polynomial-E 𝑛 𝑡 Euler-polynomial-E 𝑚 𝑡 𝑡 superscript 1 𝑛 4 superscript 2 𝑚 𝑛 2 1 𝑚 𝑛 𝑚 𝑛 2 Bernoulli-number-B 𝑚 𝑛 2 {\displaystyle{\displaystyle\int_{0}^{1}E_{n}\left(t\right)E_{m}\left(t\right)% \mathrm{d}t=(-1)^{n}4\frac{(2^{m+n+2}-1)m!n!}{(m+n+2)!}B_{m+n+2}.}}
    0 references
    DLMF id
    DLMF:24.13.E11
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1addec
    0 references
    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.m2aedec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
    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.m1jdec
    0 references
    Q12111
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1jdec
    0 references
     
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