Friday, October 19, 2012

1210.5157 (Michael A. Idowu)

Elegant expressions and generic formulas for the Riemann zeta function
for integer arguments

Michael A. Idowu
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.
View original:

1 comment:

  1. Dear Mike, I, Bill Bouris, can prove to you that zeta(2n+1) can't and won't have a closed form. I will show you how it can be written infinitely many different ways. Please contact me at, and I will supply the proof to you. also, you can find it on the first page of my website... further down the page... I can also supply you with an Excel speadsheet of two examples to make my proof more concrete. it's not written in LaTeX, but it's simple enough for an eighth-grader to understand. I'm just counting the fractions. Bill