On the convergence of series of translated functions and applications

The present work presents some necessary and sufficient conditions for the convergence to a periodic function of a special kind of function series defined by ∑j=0∞f(t−jd), where f:R↦R+∪{0}f:R↦R+∪{0} with f(t)=0f(t)=0 for t<0t<0. It also discusses some biological applications that can be derived from these results, by considering each f(t−jd)f(t−jd) as describing an isolated effect related to an application at time jdjd, and the sum of them as an accumulated effect.