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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:
11S40Zeta functions and L-functions of local number fields
11S80Other analytic theory of local fields
11B68Bernoulli and Euler numbers and polynomials