DLMF:24.14.E3 (Q7548)

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DLMF:24.14.E3
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    ∑ k = 0 n ( n k ) ⁢ E k ⁡ ( h ) ⁢ E n - k ⁡ ( x ) = 2 ⁢ ( E n + 1 ⁡ ( x + h ) - ( x + h - 1 ) ⁢ E n ⁡ ( x + h ) ) , superscript subscript 𝑘 0 𝑛 binomial 𝑛 𝑘 Euler-polynomial-E 𝑘 ℎ Euler-polynomial-E 𝑛 𝑘 𝑥 2 Euler-polynomial-E 𝑛 1 𝑥 ℎ 𝑥 ℎ 1 Euler-polynomial-E 𝑛 𝑥 ℎ {\displaystyle{\displaystyle\sum_{k=0}^{n}{n\choose k}E_{k}\left(h\right)E_{n-% k}\left(x\right)=2(E_{n+1}\left(x+h\right)-(x+h-1)E_{n}\left(x+h\right)),}}
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    DLMF:24.14.E3
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