Neumann series

A Neumann series is a series for the inverse of 1 - x in a Banach algebra. Thus

$(1 - x)^{-1} = \sum_{k=0}^\infty x^k$

where the series is absolutely convergent if x has norm less than 1. The series is named after Carl Neumann.

The Neumann series forms the basis for the Liouville-Neumann series, which is used to solve Fredholm integral equations.

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