International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 583-587
Some series whose coefficients involve the value for $n$ odd
Department of Mathematical Sciences, Oakland University, Rochester 48309, Michigan, USA
Received 10 September 1986
Copyright © 1989 L. R. Bragg. 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.
By using two basic formulas for the digamma function, we derive a variety
of series that involve as coefficients the values , 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.