On rapidly convergent series expressions for zeta- and L-values, and log sine integrals

Regarding the rapidly convergent series expansion for special values of zeta- and L-functions for integer points, there are two approaches. One approach starts from Euler's 1772 formula for zeta (3) and culminates in Srivastava's very recent results via many intermediate results, and the other is due to Wilton's investigation, which was shown by us (Aeq. Math. 59, 2000, 1-19) to be a consequence of Ramanujan's work (Collected Papers of Srinivasa Ramanujan, CUP 1927, reprint Chelsea, 1962, pp. 163-168). More recently, Katsurada (Acta Arith. 90, 1999, 79-89.) has generalized all existing formulas into a rather wide framework of Dirichlet L-functions. Our purpose is to show that even the most general Katsurada's formulas are easy consequences of our fundamental summation formulas for the series with Hurwitz zeta-function coefficients. We give a three-line proof of Katsurada's main theorem, and also we make some remarks on the recent paper of Bradley (The Ramanujan J. 3, 1999, 159-173).