Demystification of Taylor,Laurent coefficients of Lerch,Hurwitz Zeta functions and Dirichlet L-Function at Unity and Zero and their Bounds

Vivek V. Rane

Published 2008-12-07Version 1

Using elementary methods,we obtain simple,explicit expressions and bounds of higher order derivatives of Hurwitz zeta function and consequently those of Dirichlet L-function and also,of Lerch's Zeta function at unity (and at Zero too)and also obtain their interrelations.We also state elementary complete forms of approximate functional equations of Hurwitz zeta function and Dirichlet L-function in the critical strip.