Some calculations related to the Riemann Zeta function for integer values Paul Eloe University of Dayton Abstract: ( ) ∑ ( ) is the Riemann Zeta function. If , an even integer, ( ) can be calculated, recursively. Methods are not known to calculate ( ) if , an odd integer. We show some calculations for and then derive a viable method to approximate ( ) using the values for ( ). Some historical context is given.