One of the very useful series that show up in physics is the riemann zeta function 1 1 i ()5 4 32 where z > 1 (as you know, it does not converge for r 1). these series show up often in + +. (1) statistical mechanics, for example. show that u-1 du roo c)t(e (2) where the gamma function r() for r> 0 is given by r(z) jo (3) the integral in eq.(2) is related so-called bose-einstein integrals.