Integral Difference Ratio Functions on Integers

Abstract

Abstract. Various problems lead to the same class of functions from integers to integers: functions having integral difference ratio, i.e. verifyingIn this paper we characterize this class of functions from Z to Z via theirà la Newton series expansions on a suitably chosen basis of polynomials (with rational coefficients). We also exhibit an example of such a function which is not polynomial but Bessel like.