Abstract
This chapter deals with evaluations and representations of the Riemann zeta function ζ(s). The evaluation of ζ(s) is based on the solution of the Basler problem, which is available in various forms. Along with Euler's result, various convergent series expressions for ζ(s) are described in this chapter. In this chapter, computationally useful cases are considered. In one of the cases, it is observed that ζ(s) can be represented by means of a series, which converges much more rapidly than that in Euler's celebrated formula and the one used by Apery. Symbolic and numeric computations using Mathematica for Linux show, among other things, that only 50 terms of the series are capable of producing an accuracy of seven decimal places.
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