Summation equation

In mathematics, a summation equation or discrete integral equation is an equation in which an unknown function appears under a summation sign. The theories of summation equations and integral equations can be unified as integral equations on time scales^[1] using time scale calculus. A summation equation compares to a difference equation as an integral equation compares to a differential equation.

The Volterra summation equation is: $${\displaystyle x(t)=f(t)+\sum _{s=m}^{n}k{\bigl (}t,s,x(s){\bigr )}}$$ where x is the unknown function, s, t are integers, and f, k are known functions.