Derivatives of the Hurwitz Zeta function for rational arguments

[摘要] The functional equation for the Hurwitz Zeta function zeta(s,a) is used to obtain formulas for derivatives of zeta(s,a) at negative odd s and rational a. For several of these rational arguments, closed-form expressions are given in terms of simpler transcendental functions, like the logarithm, the polygamma function, and the Riemann Zeta function. (C) 1998 Elsevier Science B.V. All rights reserved.

[发布日期] 1998-12-21

[关键词] Hurwitz Zeta function;transcendental functions;polygamma function