DLMF:24.4.E19 (Q7432)

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DLMF:24.4.E19
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    E n ( m x ) = - 2 m n n + 1 k = 0 m - 1 ( - 1 ) k B n + 1 ( x + k m ) , Euler-polynomial-E 𝑛 𝑚 𝑥 2 superscript 𝑚 𝑛 𝑛 1 superscript subscript 𝑘 0 𝑚 1 superscript 1 𝑘 Bernoulli-polynomial-B 𝑛 1 𝑥 𝑘 𝑚 {\displaystyle{\displaystyle E_{n}\left(mx\right)=-\frac{2m^{n}}{n+1}\sum_{k=0% }^{m-1}(-1)^{k}B_{n+1}\left(x+\frac{k}{m}\right),}}
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    DLMF:24.4.E19
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    m = 2 , 4 , 6 , 𝑚 2 4 6 {\displaystyle{\displaystyle m=2,4,6,\dots}}
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    B n ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    C24.S2.SS1.m2agdec
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    E n ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    C24.S2.SS2.m2agdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C24.S1.XMD2.m1ldec
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    m 𝑚 {\displaystyle{\displaystyle m}}
    C24.S1.XMD4.m1fdec
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