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Hypergeometric series associated
with the Hurwitz-Lerch zeta function
Received: May 26, 2008; Revised: September 11, 2008; Accepted: September 25, 2008
Abstract. The present work is sequel to the papers  and , 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.
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