Liouville-Neumann series

In mathematics, the Liouville–Neumann series is an infinite series that corresponds to the resolvent formalism technique of solving the Fredholm integral equations in Fredholm theory.

The Liouville–Neumann (iterative) series is defined as

which, provided that ${\displaystyle \lambda }$ is small enough so that the series converges, is the unique continuous solution of the Fredholm integral equation of the second kind,

${\displaystyle f(t)=\phi (t)-\lambda \int _{a}^{b}K(t,s)\phi (s)\,ds.}$

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