On the similar order of convergence of two adjacent sequences related to ζ(1/2)

  • Authors:

  • Andrei Vernescu

  • Affiliations:

  • Valahia University, Department of Mathematics, Târgovişte, Romania

  • Venue:
  • MMACTEE'06 Proceedings of the 8th WSEAS international conference on Mathematical methods and computational techniques in electrical engineering
  • Year:
  • 2006

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Abstract

In this paper we prove the following similar two-sided estimations 1/2√n+1 n - l and 1/2√n+1 n , where an = (Σl=1 n 1/√k) - 2√n+1, bn = (Σ l=1 n 1/√k) - 2√n, and l = lim n→∞ an = lim n→∞ bn= ζ(1/2) = -1,46035... (ζ(1/2) being considered in the sense of analytic continuation). These sequences are adjacent. We give a definition of adjacence. Classification Subject AMS: 26D15, 30B10, 33F05, 40A05.