IJPAM: Volume 96, No. 3 (2014)
THE STOLZ-CESÀRO LEMMA
Distrito Telefónica
Edificio Este 1
28050 Madrid, SPAIN
Abstract. In this paper, we consider the hypersum polynomial
, which is a generalization of the polynomial associated with the sums of powers of integers
. Using the Stolz-Cesàro lemma, we derive an explicit
formula for the set of coefficients
in terms of
and the Bernoulli numbers. This allows us to obtain the
-th order hypersum
once the
-th order hypersum
is known. Moreover, we show how to obtain
from
.
Received: June 24, 2014
AMS Subject Classification: 11B57, 11C08
Key Words and Phrases: sums of powers of integers, hypersum polynomial, Stolz-Cesàro lemma
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DOI: 10.12732/ijpam.v96i3.5 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 96
Issue: 3
Pages: 343 - 351
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This work is licensed under the Creative Commons Attribution International License (CC BY).