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arXiv · 1403.0435

Recurrence formulas with gaps for Bernoulli and Euler polynomials

Zhi-Hong Sun
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Abstract

Let $\{B_n\}$, $\{B_n(x)\}$ and $\{E_n(x)\}$ be the Bernoulli numbers, Bernoulli polynomials and Euler polynomials, respectively. In this paper we mainly establish formulas for $\sum_{6\mid k-3}\binom nkB_{n-k}(x)$, $\sum_{6\mid k}\binom nkE_{n-k}(x)$ and $\sum_{6\mid k-3}\binom nkm^kB_{n-k}$ in the cases $m=2,3,4$.

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Zhi-Hong Sun. 2014-03-03. Recurrence formulas with gaps for Bernoulli and Euler polynomials. https://arxiv.org/abs/1403.0435

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