Explicit Formulas for Some Rational Weighted Sums of Powers of Integers

摘要

In this article we consider weighted sums of the form, where f_p (k) is a polynomial of degree p, and λ is a rational weight. For some concrete f_p (k) (quadratic, some cubic, and some more of degree 4), and some concrete weights λ, we obtain explicit expressions for the corresponding weighted sums in terms of the binomial coefficients (_p~(n+s)), s = 1,2,..., p.