Asymptotic Distribution of Zeros of a Certain Class of Hypergeometric Polynomialsd
Number of Authors: 2
2016 (English)In: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 16, no 2, 167-185 p.Article in journal (Refereed) Published
We study the asymptotic behavior of the zeros of a family of a certain class of hypergeometric polynomials [GRAPHICS] , using the associated hypergeometric differential equation, as the parameters go to infinity. The curve configuration on which the zeros cluster is characterized as level curves associated with integrals on an algebraic curve. The algebraic curve is the hypergeometrc differential equation, using a similar approach to the method used in Borcea et al. (Publ Res Inst Math Sci 45(2):525-568, 2009). In a specific degenerate case, we make a conjecture that generalizes work in Boggs and Duren (Comput Methods Funct Theory 1(1):275-287, 2001), Driver and Duren (Algorithms 21(1-4):147-156, 1999), and Duren and Guillou (J Approx Theory 111(2):329-343, 2001), and present experimental evidence to substantiate it.
Place, publisher, year, edition, pages
2016. Vol. 16, no 2, 167-185 p.
Hypergeometric polynomials, Cauchy transform, Asymptotic zero measures, Hypergeometric differential equation
IdentifiersURN: urn:nbn:se:su:diva-132045DOI: 10.1007/s40315-015-0131-1ISI: 000376502200001OAI: oai:DiVA.org:su-132045DiVA: diva2:948945