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 scalesVolterra integral equations on time scales: Basic qualitative and quantitative results with applications to initial value problems on unbounded domains, Tomasia Kulik, Christopher C. Tisdell, September 3, 2007 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:
where is the unknown function, are integers, and are known functions.
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Summation equations or discrete integral equations