International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 421478, 20 pages
doi:10.1155/2008/421478
Relations among sums of reciprocal powers. II.
José María Amigó
Centro de Investigación Operativa, Universidad Miguel Hernández, Avenida de la Universidad s/n, 03202 Elche (Alicante), Spain
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.