DLMF:24.13.E11 (Q7545): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1jdec

Revision as of 01:45, 2 January 2020

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DLMF:24.13.E11
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    Statements

    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}.}}
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    DLMF:24.13.E11
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    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    C24.S2.SS1.m1addec
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    E n ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    C24.S2.SS2.m2aedec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1ajdec
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5aadec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3ajdec
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    m 𝑚 {\displaystyle{\displaystyle m}}
    C24.S1.XMD4.m1adec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C24.S1.XMD5.m1jdec
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