On Lucas-balancing zeta function
Keywords:Riemann zeta function, balancing zeta function, Lucas-balancing zeta function, balancing L-function, Lucas-balancing L-function
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.