A new series representation for &zgr;(3)
American Mathematical Monthly
Further series representations for &zgr;(2n + 1)
Applied Mathematics and Computation
A certain class of rapidly convergent series representations for &zgr;(2n+1)
Journal of Computational and Applied Mathematics - Special issue on higher transcendental functions and their applications
Computational strategies for the Riemann zeta function
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Recurrence for values of the zeta function
Applied Numerical Mathematics
Summation of divergent power series by means of factorial series
Applied Numerical Mathematics
Computers & Mathematics with Applications
Family of curves based on Riemann zeta function
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part IV
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A fascinatingly large number of seemingly independent solutions of the so-called Basler problem of evaluating the Riemann Zeta function ζ(s) when s= 2, which was of vital importance to Leonhard Euler (1707-1783) and the Bernoulli brothers (Jakob Bernoulli (1654-1705) and Johann Bernoulli (1667-1748)), have appeared in themathematical literature ever since Euler first solved this problem in the year 1736. The main object of this two-part series of lectures is to present some recent developments on the evaluations and representations of ζ(s) when s ∈ N \ {1}, N being the set of natural numbers. We emphasize upon several interesting classes of rapidly convergent series representations for ζ(2n+ 1) (n∈ N) which have been developed in recent years. In two of many computationally useful special cases considered here, it is observed that ζ(3) can be represented by means of series which converge much more rapidly than that in Euler's celebrated formula as well as the series used recently by Roger Apéry (1916-1994) in his proof of the irrationality of ζ(3). Symbolic and numerical computations using Mathematica (Version 4.0) for Linux show, among other things, that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places.