## On interpolation functions of the twisted generalized Frobenius-Euler numbers.(English)Zbl 1217.11115

Summary: The main purpose of this paper is to apply the Mellin transform to the generating functions of $$q$$-generalized Frobenius-Euler numbers and twisted $$q$$-generalized Frobenius-Euler numbers. By using this result, we define an integral representation of twisted $$l_{H,q}$$-functions, which interpolates twisted $$q$$-generalized Frobenius-Euler numbers at negative integers. We also define twisted $$q$$-zeta functions. Furthermore, we give a relation between twisted $$l_{H,q}$$-functions and twisted $$q$$-zeta functions. We obtain new results related to the twisted $$l_{H,q}$$-function as well.

### MSC:

 11S40 Zeta functions and $$L$$-functions 11S80 Other analytic theory (analogues of beta and gamma functions, $$p$$-adic integration, etc.) 11B68 Bernoulli and Euler numbers and polynomials