On Lucas-balancing zeta function

  • Debismita Behera Department of Mathematics, Veer Surendra Sai University of Technology, Burla-768018
  • Utkal Keshari Dutta Department of Mathematics, Veer Surendra Sai University of Technology, Burla-768018
  • Prasanta Kumar Ray School of Mathematical Sciences, Sambalpur University, Jyoti Vihar, Burla- 768019
Keywords: Riemann zeta function, balancing zeta function, Lucas-balancing zeta function, balancing L-function, Lucas-balancing L-function

Abstract

In the present study a new modication of Riemann zeta function known as Lucas-balancing zeta function is introduced. The Lucas-balancing zeta function admits its analytic continuation over the whole complex plane except its poles. This series converges to a fixed rational number − ½ at negative odd integers. Further, in accordance to Dirichlet L-function, the analytic continuation of Lucas-balancing L-function is also discussed.

Published
2018-06-10
Section
Articles