Formulas for higher derivatives of the Riemann zeta function

Abstract

The functional equation for ζ ( s ) \zeta (s) is used to obtain formulas for all derivatives ζ ( k ) ( s ) {\zeta ^{(k)}}(s) . A closed form evaluation of ζ ( k ) ( 0 ) {\zeta ^{(k)}}(0) is given, and numerical values are computed to 15D for k = 0 ( 1 ) 18 k = 0(1)18 .