  Already in 1734 Euler found a short explicit formula for the value of Riemann
zeta function Zeta(s) when the argument s equals a positive integer 2n where
n=1,2,3,. No such formula exists for odd positive integer arguments of Zeta.
The present paper discusses in particular the case of Zeta(3). A formula for
Zeta(3) is obtained which in addition to a number of well known constants
includes a rapidly converging infinite series, of which each term contains
rational numbers and an even power of Pi. An attempt to convert this series
into a finite number of terms containing commonly known constants is met with
only partial success. The general case for zeta(2n+1) is also worked out.
