Elegant expressions and generic formulas for the Riemann zeta function for integer arguments
Number Theory
2015-01-06 v1 Classical Analysis and ODEs
Abstract
A new definition for the Riemann zeta function for all positive integer number s > 1 is presented. We discover a most elegant expression and easy method for calculating the Riemann zeta function for small even integer values. Through this new reformulation we provide a one-line proof of the value of zeta(2) and demonstrate that zeta(2s) may be calculated by hand using only the cotangent function when the magnitude of the integer s is small.
Cite
@article{arxiv.1210.5157,
title = {Elegant expressions and generic formulas for the Riemann zeta function for integer arguments},
author = {Michael A. Idowu},
journal= {arXiv preprint arXiv:1210.5157},
year = {2015}
}