HYPERSUMS OF POWERS OF INTEGERS VIA THE STOLZ-CESARO LEMMA
Jose Luis Cereceda · International Journal of Pure and Apllied Mathematics · 2014
In this paper, we consider the hypersum polynomial Pc r k,m n r , which is a generalization of the polynomial associated with the sums of powers of integersUsing the Stolz-Cesàro lemma, we derive an explicit formula for the set of coefficients {c r k,m } k+m+1 r=1 in terms of {c r k,m-1 } k+m r=1 and the Bernoulli numbers.This allows us to obtain the m-th order hypersum P (m) k (n) once the (m -1)-th order hypersum P (m-1) k (n) is known.Moreover, we show how to obtain P (m) k (n) from P (m) k-1 (n).