In mathematics, the Liouville–Neumann series is a function series that results from applying the resolvent formalism to solve Fredholm integral equations in Fredholm theory.
is small enough so that the series converges, is the unique continuous solution of the Fredholm integral equation of the second kind,
The resolvent, also called the "solution kernel" for the integral operator, is then given by a generalization of the geometric series, where K0 is again δ(x−z).
The solution of the integral equation thus becomes simply Similar methods may be used to solve the Volterra integral equations.
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