Asymptotics of Racah polynomials with fixed parameters
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- by X.-S. Wang and R. Wong PDF
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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.References
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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
- MR Author ID: 192744
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1083-1096
- MSC (2010): Primary 41A60; Secondary 33C45
- DOI: https://doi.org/10.1090/proc/13771
- MathSciNet review: 3750220