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Formulas for higher derivatives of the Riemann zeta function. (English) Zbl 0557.10029
The paper contains a new formula for (-1) k ζ (k) (1-s), which enables the author to determine explicitly the coefficients a jkm and b jkm of a previous formula of a similar kind due to R. Spira [J. Lond. Math. Soc. 40, 677-682 (1965; Zbl 0147.305)]. As a consequence, a closed form evaluation of ζ (k) (0) is obtained. The results about ζ (k) (0) contain the well known formulae when k=1,2, and appear to be new if k3. Numerical values are given for k=1,···,18.
Reviewer: A.Perelli
MSC:
11M06ζ(s) and L(s,χ)