Polygamma functions of negative order

Liouville's fractional integration is used to define polygamma functions ~,(")(z) for negative integer n. It is shown that such ~k(n)(z) can be represented in a closed form by means of the first derivatives of the Hurwitz Zeta function. Relations to the Barnes G-function and generalized Glaisher's constants are also discussed. (~) 1998 Elsevier Science B.V. All rights reserved.