International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 421478, 20 pages
Relations among Sums of Reciprocal Powers—Part II
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.
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.