Some Definite Integrals Associated with the Riemann Zeta Function

The authors aim at deriving a family of series representations for ζ(2n + 1)(n ∊ N) by evaluating certain trigonometric integrals in several different ways. They also show how the results presented in this paper relate to those that were obtained in other works. Finally, some illustrative computational examples, using Mathematica (Version 4.0) for Linux, are considered