TITLE: Can a polynomial be expressed as an infinite sum of non-polynomial functions?
QUESTION [8 upvotes]: The Taylor series represents a non-polynomial function as an infinite series of polynomials, so is it possible to express a polynomial function as an infinite series of non-polynomial functions?

REPLY [2 votes]: Consider the sum of the sequence of characteristic functions of all intervals [n,n+1) for all integers n. None of these functions is a polynomial, yet their sum is one.