International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 421478, 20 pages
doi:10.1155/2008/421478
Research Article

Relations among Sums of Reciprocal Powers—Part II

José María Amigó

Centro de Investigación Operativa, Universidad Miguel Hernández, Avenida de la Universidad s/n, 03202 Elche (Alicante), Spain

Received 18 July 2008; Accepted 10 September 2008

Academic Editor: Pentti Haukkanen

Copyright © 2008 José María Amigó. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some formulas relating the classical sums of reciprocal powers are derived in a compact way by using generating functions. These relations can be conveniently written by means of certain numbers which satisfy simple summation formulas. The properties of the generating functions can be further used to easily calculate several series involving the classical sums of reciprocal powers.