Note: You will need a computer to do this unless you plan on writing out pages of calculations for just a few values. This will detail how to calculate a value of the analytic continuation of the zeta function: First we will calculate: for a finite (hopefully large) value of n so We then have to calculate one value of if s is a complex number we can use Euler's formula because we have after this calculation we will have a complex number in the denominator to get it to the numerator multiply by the complex conjugate the resulting complex number has this can simply be added to any values for n that were calculated before. Now we calculate This can be done with calculation similar to the previous one but noting that and finally multiply the two complex numbers together.