Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Fourier expansion in cylindrical coordinates for the
  three-dimensional Helmholtz Green function   A new method is presented for Fourier decomposition of the Helmholtz Green
Function in cylindrical coordinates, which is equivalent to obtaining the
solution of the Helmholtz equation for a general ring source. The Fourier
coefficients of the Helmholtz Green function are split into their half
advanced+half retarded and half advanced-half retarded components. Closed form
solutions are given for these components in terms of a Horn function and a
Kampe de Feriet function, respectively. The systems of partial differential
equations associated with these two-dimensional hypergeometric functions are
used to construct a fourth-order ordinary differential equation which both
components satisfy. A second fourth-order ordinary differential equation for
the general Fourier coefficent is derived from an integral representation of
the coefficient, and both differential equations are shown to be equivalent.
Series solutions for the various Fourier coefficients are also given, mostly in
terms of Legendre functions and Bessel/Hankel functions. These are derived from
the closed form hypergeometric solutions or an integral representation, or
both. Numerical calculations comparing different methods of calculating the
Fourier coefficients are presented.

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The categories of this paper are: patt-sol
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The categories of this paper are: eess
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an