Inductive construction of rapidly convergent series representations for ?(2>n> + 1)

For a natural number n, the authors propose and develop a method of inductive construction of several (presumably new) rapidly convergent series representations for the values of the Riemann Zeta function ζ(2n + 1). Under a certain assumption, the various series representations for ζ(2n + 1), which are derived here by using this method, converge remarkably rapidly with their general terms having the order estimate: O(k ^−2n−m · 2^−2k ) (k → ∞), where m is an arbitrary natural number. Numerical and symbolic computational aspects of some of the results presented here are also considered.

Keywords:

• Riemann And Hurwitz Zeta Functions
• Bernoulli Numbers
• Harmonic Numbers
• Series Representations
• Order Estimates
• Mellin Transformation