DLMF:24.17.E1 (Q7584)

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DLMF:24.17.E1
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    j = a n - 1 ( - 1 ) j f ( j + h ) = 1 2 k = 0 m - 1 E k ( h ) k ! ( ( - 1 ) n - 1 f ( k ) ( n ) + ( - 1 ) a f ( k ) ( a ) ) + R m ( n ) , superscript subscript 𝑗 𝑎 𝑛 1 superscript 1 𝑗 𝑓 𝑗 1 2 superscript subscript 𝑘 0 𝑚 1 Euler-polynomial-E 𝑘 𝑘 superscript 1 𝑛 1 superscript 𝑓 𝑘 𝑛 superscript 1 𝑎 superscript 𝑓 𝑘 𝑎 subscript 𝑅 𝑚 𝑛 {\displaystyle{\displaystyle\sum_{j=a}^{n-1}(-1)^{j}f(j+h)=\frac{1}{2}\sum_{k=% 0}^{m-1}\frac{E_{k}\left(h\right)}{k!}\left((-1)^{n-1}f^{(k)}(n)+(-1)^{a}f^{(k% )}(a)\right)+R_{m}(n),}}
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    DLMF:24.17.E1
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    E n ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    C24.S2.SS2.m2adec
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5adec
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    j 𝑗 {\displaystyle{\displaystyle j}}
    C24.S1.XMD1.m1dec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C24.S1.XMD2.m1dec
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    m 𝑚 {\displaystyle{\displaystyle m}}
    C24.S1.XMD4.m1dec
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    h {\displaystyle{\displaystyle h}}
    C24.S17.XMD1.m1dec
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    a 𝑎 {\displaystyle{\displaystyle a}}
    C24.S17.XMD2.m1dec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C24.S17.XMD3.m1dec
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