Abstract
In this paper, we focus on four weights
where
,
,
, N>0;
where
,
,
;
with
,
,
,
, where
is the Heaviside step function; and
with
,
, N>0,
. The second-order differential equations satisfied by
, the degree-n polynomials orthogonal with respect to each of these weights, are shown to be asymptotically equivalent to the bi-confluent Heun equations as
. In most cases, a parameter other than n must simultaneously be sent to a limiting value.
Acknowledgments
D. Wang, M. Zhu and Y. Chen would like to give thanks the Science and Technology Development Fund of the Macau SAR for providing FDCT 023/2017/A1. They would also like to thank the University of Macau for MYRG 2018-00125 FST.
Disclosure statement
No potential conflict of interest was reported by the authors.