535 research outputs found
Zeros of linear combinations of Laguerre polynomials from different sequences
We study interlacing properties of the zeros of two types of linear
combinations of Laguerre polynomials with different parameters, namely
and .
Proofs and numerical counterexamples are given in situations where the zeros of
, and , respectively, interlace (or do not in general) with the zeros
of , , or . The results we prove hold
for continuous, as well as integral, shifts of the parameter
Exceptional Laguerre polynomials
The aim of this paper is to present the construction of exceptional Laguerre
polynomials in a systematic way, and to provide new asymptotic results on the
location of the zeros. To describe the exceptional Laguerre polynomials we
associate them with two partitions. We find that the use of partitions is an
elegant way to express these polynomials and we restate some of their known
properties in terms of partitions. We discuss the asymptotic behavior of the
regular zeros and the exceptional zeros of exceptional Laguerre polynomials as
the degree tends to infinity.Comment: To appear in Studies in Applied Mathematic
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