In mathematics, the Neumann polynomials, introduced by Carl Neumann for the special case
, are a sequence of polynomials in
used to expand functions in term of Bessel functions.[1]
The first few polynomials are





A general form for the polynomial is

and they have the "generating function"

where J are Bessel functions.
To expand a function f in the form

for
, compute

where
and c is the distance of the nearest singularity of f(z) from
.