Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On subnormal solutions of periodic non-homogeneous linear differential
  equations, special functions and special polynomials   This paper offers a new and complete description of subnormal solutions of
certain non-homogeneous second order periodic linear differential equations
first studied by Gundersen and Steinbart in 1994. We have established a
previously unknown relation that the general solutions (\textit{i.e.}, whether
subnormal or not) of the DEs can be solved explicitly in terms of classical
special functions, namely the Bessel, Lommel and Struve functions, which are
important because of their numerous physical applications. In particular, we
show that the subnormal solutions are written explicitly in terms of the
degenerate Lommel functions $S_{\mu, \nu}(\zeta)$ and several classical special
polynomials related to the Bessel functions. In fact, we solve an equivalent
problem in special functions that each branch of the Lommel function $S_{\mu,
\nu}(\zeta)$ degenerates if and only if $S_{\mu, \nu}({\rm e}^z)$ has finite
order of growth in $\mathbf{C}$. We achieve this goal by proving new properties
and identities for these functions. A number of semi-classical
quantization-type results are obtained as consequences. Thus our results not
only recover and extend the result of Gundersen and Steinbart \cite{GS94}, but
the new identities and properties found for the Lommel functions are of
independent interest in a wider context.

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The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci