Asymptotics of Racah polynomials with fixed parameters

Asymptotics of Racah polynomials with fixed parameters

In this paper, we investigate asymptotic behaviors of Racah polynomials with fixed parameters and scaled variable as the polynomial degree tends to infinity. We start from the difference equation satisfied by the polynomials and derive an asymptotic formula in the outer region via ratio asymptotics....

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society Vol. 146; no. 3; pp. 1083 - 1096
Main Authors: WANG, X.-S., WONG, R.
Format: Journal Article
Language:English
Published: American Mathematical Society 01-03-2018
Subjects:
B. ANALYSIS
matching principle
Asymptotics
Racah polynomials
difference equations
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Summary:In this paper, we investigate asymptotic behaviors of Racah polynomials with fixed parameters and scaled variable as the polynomial degree tends to infinity. We start from the difference equation satisfied by the polynomials and derive an asymptotic formula in the outer region via ratio asymptotics. Next, we find the asymptotic formulas in the oscillatory region via a simple matching principle. Unlike the varying parameter case considered in a previous paper, the zeros of Racah polynomials with fixed parameters may not always be real. For this unusual case, we also provide a standard method to determine the oscillatory curve which attracts the zeros of Racah polynomials when the degree becomes large.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13771