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International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 583-587
http://dx.doi.org/10.1155/S0161171289000712

Some series whose coefficients involve the value ζ(n) for $n$n odd

Department of Mathematical Sciences, Oakland University, Rochester 48309, Michigan, USA

Received 10 September 1986

Copyright © 1989 Hindawi Publishing Corporation. 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

By using two basic formulas for the digamma function, we derive a variety of series that involve as coefficients the values (2n+1), n=1,2,, of the Riemann-zeta function. A number of these have a combinatorial flavor which we also express in a trignometric form for special choices of the underlying variable. We briefly touch upon their use in the representation of solutions of the wave equation.