Making a connection between zeta(3) and zeta(6)

There is no known ‘closed form’ expressions for the Riemann zeta function at odd positive integers similar to the even integers.  It is not known whether the pattern with the even powers of the constant π extends to the odd integers.  After more than 300 hundred years of the best minds in mathematics trying to solve this riddle, not much headway has been made. I recall reading in posting in Stack Exchange that there is not likely any obvious relationship between the odd and even integer zeta values.  The following article explores how to find the values of zeta for the even integers using Fourier series.  It also makes a connection between the even and odd zeta values using a manipulation of Fourier series. Read more…Fourier Series and zeta(n)