On generalized Dedekind sums involving quasi-periodic Euler functions

The aim of this paper is to give a simple proof for a reciprocity law of generalized Dedekind sums involving quasi-periodic Euler functions by considering the analytic properties of Euler polynomials which is an analogue of the reciprocity law of the classical Dedekind sums dating back to Dedekind [13] in 1892. We also derive an explicit expression for generalized Dedekind sums involving quasi-periodic Euler functions.