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Uniform treatment of Darboux's method and the Heisenberg polynomials


Authors: Sai-Yu Liu, R. Wong and Yu-Qiu Zhao
Journal: Proc. Amer. Math. Soc. 141 (2013), 2683-2691
MSC (2010): Primary 41A60; Secondary 33C15
Published electronically: March 29, 2013
MathSciNet review: 3056558
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Abstract: We show that the set of Heisenberg polynomials furnishes a simple non-trivial example in the uniform treatment of Darboux's method.


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Sai-Yu Liu
Affiliation: Department of Mathematics, ZhongShan University, GuangZhou 510275, People’s Republic of China

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

Yu-Qiu Zhao
Affiliation: Department of Mathematics, ZhongShan University, GuangZhou 510275, People’s Republic of China
Email: stszyq@mail.sysu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2013-11587-X
Keywords: Heisenberg polynomials, Darboux's method, uniform asymptotic expansion, confluent hypergeometric function, Bessel function
Received by editor(s): August 18, 2011
Received by editor(s) in revised form: October 22, 2011
Published electronically: March 29, 2013
Additional Notes: The research of the third author was supported in part by the National Natural Science Foundation of China under grant numbers 10471154 and 10871212
Communicated by: Walter Van Assche
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.