An odd-power identity involving discrete convolution
Petro Kolosov · Figshare · 2016
Abstract: In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between m-order polynomials in T ∑lk=1 ∑jm=0 Am,jkj(T-k)j=∑mk=0 (-1)m-k Um(l,k)∙Tk = T2m+1 Related OEIS sequences: A287326, A300656, A300785, A302971, A304042, A316349, A316387arXiv version: https://arxiv.org/abs/1603.02468 Keywords: Faulhaber's formula, Faulhaber's theorem, Binomial Theorem, Binomial coefficient, Binomial distribution, Binomial identities, Power Sums, Finite differences MSC classes: 11C08, 41A10 See also: https://kolosovpetro.github.io/ https://orcid.org/0000-0002-6544-8880