The Neumann series of a bounded operator 
on a Banach
space is
 |
Here 
,
where 
is the identity operator. If 
, the series converges
in the operator norm and
 |
which is analogous to the geometric series. When 
is integration against an integral
kernel, the same construction gives an integral
equation Neumann series. A Bessel
function Neumann series is a different type of series
expansion in Bessel functions.
