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 from .
^Abramowitz and Stegun, p. 363, 9.1.82 ff.
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