On Evaluation of the Dirichlet Series at Positive Integers by q-Calculation Original Research Article

By q-calculation, we prove some recursion formulas for the values of Riemann ζ-function ζ(s) at positive even integers, and also prove some series representation for the values of ζ(s) at positive odd integers. By using these relations, we evaluate the Dirichlet L-series at positive integers.