Uniform asymptotic expansions of the TricomiCarlitz polynomials
Authors:
K. F. Lee and R. Wong
Journal:
Proc. Amer. Math. Soc. 138 (2010), 25132519
MSC (2010):
Primary 41A60, 39A10; Secondary 33C45
Published electronically:
March 4, 2010
MathSciNet review:
2607881
Fulltext PDF
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Additional Information
Abstract: The TricomiCarlitz polynomials satisfy the secondorder linear difference equation with initial values and , where is a real variable and is a positive parameter. An asymptotic expansion is derived for these polynomials by using the turningpoint theory for threeterm recurrence relations developed by Wang and Wong [Numer. Math. 91(2002) and 94(2003)]. The result holds uniformly in regions containing the critical values , where .
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 J.L. López and N.M. Temme, Approximation of orthogonal polynomials in terms of Hermite polynomials. Dedicated to Richard A. Askey on the occasion of his 65th birthday, Part II, Methods Appl. Anal., 6, 131146, 1999. MR 1803886 (2001m:33013)
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Additional Information
K. F. Lee
Affiliation:
Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
Email:
charleslkf8571@gmail.com
R. Wong
Affiliation:
Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
Email:
rscwong@cityu.edu.hk
DOI:
http://dx.doi.org/10.1090/S0002993910103013
Keywords:
TricomiCarlitz polynomials,
uniform asymptotic expansion,
difference equation
Received by editor(s):
June 23, 2009
Received by editor(s) in revised form:
November 6, 2009
Published electronically:
March 4, 2010
Dedicated:
Dedicated to the Lord
Communicated by:
Walter Van Assche
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
