Extended Riemann Bessel functions

Pages: 121 - 130, Issue Special, August 2005

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M.T. Boudjelkha - Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, United States (email)

Abstract: In this paper we discuss the extended Riemann Bessel functions, their integral representations and series expansions in terms of Riemann zeta functions and Bessel functions. We consider also other properties such as their differential equations, recurrence relations, a recent proof of the Hurwitz type formulae and applications.

Keywords:  Bessel functions, generalized zeta function, Lerch function, Riemann zeta functions.
Mathematics Subject Classification:  11M35, 11M99, 33C10, 33E99.

Received: August 2004;      Revised: May 2005;      Published: September 2005.