A Substitution to Bernoulli Numbers in easier computation of (\zeta(2k))
  An alternative formula is presented for the evaluation of the zeta function values $\zeta(2k)$ without the need for Bernoulli numbers. Our formula is recursive, and improves the efficiency with which we can calculate large values of the zeta function. 
Srinivasan Arunachalam
math.NA math.NT