Uniform Treatment of Darboux’s Method and the Heisenberg Polynomials

Sai-Yu Liu; R. Wong; Yu-Qiu Zhao

doi:10.1142/9789811290862_0007

Uniform Treatment of Darboux’s Method and the Heisenberg Polynomials

Sai-Yu Liu
, R. Wong
, Yu-Qiu Zhao^*

^*Corresponding author for this work

Department of Mathematics

Research output: Chapters, Conference Papers, Creative and Literary Works › Reprint in book › peer-review

Abstract

Original language	English
Title of host publication	The Selected Works of Roderick S C Wong
Editors	Dan Dai, Ding-Xuan Zhou
Publisher	World Scientific Publishing Co. Pte Ltd
Pages	1606-1614
Number of pages	9
Volume	4
ISBN (Electronic)	978-981-12-9087-9 , 978-981-12-9086-2
ISBN (Print)	978-981-12-9085-5
DOIs	https://doi.org/10.1142/9789811290862_0007
Publication status	Published - 2026

Bibliographical note

This is a reprint of: Liu, S.-Y., Wong, R., & Zhao, Y.-Q. (2013). Uniform treatment of Darboux's method and the Heisenberg polynomials. Proceedings of the American Mathematical Society, 141(8), 2683-2691. https://doi.org/10.1090/S0002-9939-2013-11587-X

Funding

The research of the third author was supported in part by the National Natural Science Foundation of China under grant numbers 10471154 and 10871212.

Research Keywords

Bessel function
confluent hypergeometric function
Darboux’s method
Heisenberg polynomials
uniform asymptotic expansion

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10.1142/9789811290862_0007

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title = "Uniform Treatment of Darboux{\textquoteright}s Method and the Heisenberg Polynomials",

abstract = "We show that the set of Heisenberg polynomials furnishes a simple non-trivial example in the uniform treatment of Darboux{\textquoteright}s method. {\textcopyright} 2026 by World Scientific Publishing Co. Pte. Ltd.",

keywords = "Bessel function, confluent hypergeometric function, Darboux{\textquoteright}s method, Heisenberg polynomials, uniform asymptotic expansion",

author = "Sai-Yu Liu and R. Wong and Yu-Qiu Zhao",

note = "This is a reprint of: Liu, S.-Y., Wong, R., \& Zhao, Y.-Q. (2013). Uniform treatment of Darboux's method and the Heisenberg polynomials. Proceedings of the American Mathematical Society, 141(8), 2683-2691. https://doi.org/10.1090/S0002-9939-2013-11587-X",

year = "2026",

doi = "10.1142/9789811290862\_0007",

language = "English",

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pages = "1606--1614",

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publisher = "World Scientific Publishing Co. Pte Ltd",

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T1 - Uniform Treatment of Darboux’s Method and the Heisenberg Polynomials

AU - Liu, Sai-Yu

AU - Wong, R.

AU - Zhao, Yu-Qiu

N1 - This is a reprint of: Liu, S.-Y., Wong, R., & Zhao, Y.-Q. (2013). Uniform treatment of Darboux's method and the Heisenberg polynomials. Proceedings of the American Mathematical Society, 141(8), 2683-2691. https://doi.org/10.1090/S0002-9939-2013-11587-X

PY - 2026

Y1 - 2026

KW - Bessel function

KW - confluent hypergeometric function

KW - Darboux’s method

KW - Heisenberg polynomials

KW - uniform asymptotic expansion

UR - https://www.scopus.com/pages/publications/105042902359

UR - https://www.scopus.com/pages/publications/105042902359#tab=impact

U2 - 10.1142/9789811290862_0007

DO - 10.1142/9789811290862_0007

M3 - Reprint in book

SN - 978-981-12-9085-5

VL - 4

SP - 1606

EP - 1614

BT - The Selected Works of Roderick S C Wong

A2 - Dai, Dan

A2 - Zhou, Ding-Xuan

PB - World Scientific Publishing Co. Pte Ltd

ER -

Uniform Treatment of Darboux’s Method and the Heisenberg Polynomials

Abstract

Bibliographical note

Funding

Research Keywords

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Uniform treatment of Darboux's method and the Heisenberg polynomials

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