p. 269 - 286 Hypergeometric series associated with the Hurwitz-Lerch zeta function M.G. Bin-Saad Received: May 26, 2008; Revised: September 11, 2008; Accepted: September 25, 2008 Abstract. The present work is sequel to the papers [3] and [4], and it aims at introducing and investigating a new generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions as particular cases. We study its properties, integral representations, differential relations, series expansion and discuss the link with known results. Keywords: Barnes double zeta function; Hurwitz-Lerch zeta function; Mellin-Barnes integrals; hypergeometric functions; hypergeomteric-type generating functions. AMS Subject classification: Primary: 11M06, 11M35; Secondary: 33C20. PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |