Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial solutions of differential-difference equations   We investigate the zeros of polynomial solutions to the
differential-difference equation \[
P_{n+1}(x)=A_{n}(x)P_{n}^{\prime}(x)+B_{n}(x)P_{n}(x), n=0,1,... \] where
$A_{n}$ and $B_{n}$ are polynomials of degree at most 2 and 1 respectively. We
address the question of when the zeros are real and simple and whether the
zeros of polynomials of adjacent degree are interlacing. Our result holds for
general classes of polynomials but includes sequences of classical orthogonal
polynomials as well as Euler-Frobenius, Bell and other polynomials.

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The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph