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.


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