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Asymptotics of Racah polynomials with fixed parameters


Authors: X.-S. Wang and R. Wong
Journal: Proc. Amer. Math. Soc. 146 (2018), 1083-1096
MSC (2010): Primary 41A60; Secondary 33C45
DOI: https://doi.org/10.1090/proc/13771
Published electronically: September 28, 2017
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Abstract: 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.


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Additional Information

X.-S. Wang
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70503

R. Wong
Affiliation: Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

DOI: https://doi.org/10.1090/proc/13771
Keywords: Asymptotics, Racah polynomials, difference equations, matching principle
Received by editor(s): January 17, 2017
Received by editor(s) in revised form: April 11, 2017
Published electronically: September 28, 2017
Communicated by: Mourad Ismail
Article copyright: © Copyright 2017 American Mathematical Society

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