Login New user?  
Journal of Analysis & Number Theory
An International Journal


Volumes > Vol. 4 > No. 2


Using Known Zeta-Series to Derive the Dancs-He Series for $\,\ln{2}\,$ and $\,\zeta{(2\,n+1)}$

PP: 121-124
Fabio M. S. Lima,
In a recent work, Dancs and He found new formulas for ln2 and z (2n+1), n being a positive integer, which are expressed in terms of Euler polynomials, each containing a series that apparently can not be evaluated in closed form, distinctly from z (2n), for which the Euler’s formula allows us to write it as a rational multiple of p2n. There in that work, however, the formulas are derived through certain series manipulations, by following Tsumura’s strategy, which makes it curious—in the words of those authors themselves — the appearance of the number ln2. In this note, I show how some known zeta-series can be used to derive the Dancs-He series in an alternative manner.

  Home   About us   News   Journals   Conferences Contact us Copyright naturalspublishing.com. All Rights Reserved