TY - JOUR
T1 - Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation
AU - Juan F. Mañas-Mañas & Juan J. Moreno-Balcázar
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 535
EP - 563
PY - 2022
DA - 2022/04
SN - 12
DO - http://doi.org/10.4208/eajam.240221.130921
UR - https://global-sci.org/intro/article_detail/eajam/20406.html
KW - Sobolev orthogonal polynomials, asymptotics, algorithm, computer program.
AB - <p style="text-align: justify;">The Sobolev polynomials, which are orthogonal with respect to an inner product involving derivatives, are considered. The theory about these nonstandard polynomials has been developed along the last 40 years. The local asymptotics of these
polynomials can be described by the Mehler-Heine formulae, which connect the polynomials with the Bessel functions of the first kind. In recent years, the formulae have
been computed for discrete Sobolev orthogonal polynomials in several particular cases.
We improve various known results by unifying them. Besides, an algorithm to compute
these formulae effectively is presented. The algorithm allows to construct a computer
program based on Mathematica$^®$ language, where the corresponding Mehler-Heine formulae are automatically obtained. Applications and examples show the efficiency of the
approach developed.</p>