ON TAYLOR'S COEFFICIENTS OF THE HURWITZ ZETA FUNCTION

We find a representation for the Maclaurin coefficients zeta(n)(a) of the Hurwitz zeta function zeta(s, a) = (sic)zeta(n) (a)s(n), | s | < 1, in terms of semi-convergent series zeta(n)(a) = -1 + (sic) Bk+1(a - 1)/(k + 1)! where B-n(x) are the Bernoulli polynomials and (sic) are the (absolute) Stirling numbers of the first kind. When a = 1 this gives a representation for the coefficients of the Riemann zeta function. Our main instrument is a certain series transformation formula. A similar result is proved also for the Maclaurin coefficients of the Lerch zeta function.