A SIMPLE RECURRENCE FOR THE HIGHER DERIVATIVES OF THE HURWITZ ZETA-FUNCTION

A recurrent formula which allows the calculation of the asymptotic ser ies expansion of any derivative, zeta(m)(z,a)=partial derivative(m) ze ta(z,a)/partial derivativez(m), of the Hurwitz zeta function zeta(z,a) is obtained. In particular, the first terms of the series correspondi ng to zeta''(-n,a) in inverse powers of a are explicitly given, for n= 0,1,2,3. Knowledge of these expressions is fundamental, e.g., in the z eta-function regularization procedure.