  For Hurwitz Zeta function,we consider its Taylor series expansion about
various points as an analytic function of second variable in appropriate
discs.We show that these Taylor are all polynomials in second variable for a
non positive integral argument in first variable.On using functionalequations
this results in instant evaluation of Riemann Zeta function at positive even
integral values of its argument and of Dirichlet L series at positive integral
values of its argument,when the argument and the corresponding Dirichlet
character are both even or both odd.We also obtain finite sum expression for
any Dirichlet L series,when its argument is one.We also deal with Lerch's Zeta
function on similar lines.
