A new generalization of the Riemann zeta function and its difference equation

Abstract

Abstract We have introduced a new generalization of the Riemann zeta function. A special case of our generalization converges locally uniformly to the Riemann zeta function in the critical strip. It approximates the trivial and non-trivial zeros of the Riemann zeta function. Some properties of the generalized Riemann zeta function are investigated. The relation between the function and the general Hurwitz zeta function is exploited to deduce new identities.

Keywords

• Riemann zeta function
• Hurwitz zeta function
• Polylogarithm function
• Extended Fermi-Dirac
• Bose-Einstein