On a Functional Equation

Source abstract

We have recently discussed in (1) the general solution of a certain functional equation arising in statistical thermodynamics, and we propose in this note to deal with another functional equation arising from the same source(2). The problem is to obtain the most general function f(x) which, for all positive integral values of m, n, satifies the functional equation where where A is an arbitrary constant. It is the object of this note to prove that this is the only continuous solution.