Dyson's "Favorite" Identity and Chebyshev Polynomials of the Third and Fourth Kind

被引：3
|
作者：
Andrews, George E. [1 ]
机构：
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
来源：
ANNALS OF COMBINATORICS | 2019年 / 23卷 / 3-4期
关键词：
Partitions; Dyson's favorite identity; Bailey pairs; Bailey's lemma; Chebyshev polynomials; Mock theta functions;
D O I：
10.1007/s00026-019-00443-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The combinatorial and analytic properties of Dyson's "favorite" identity are studied in detail. In particular, a q-series analog of the anti-telescoping method is used to provide a new proof of Dyson's results with mock theta functions popping up in intermediate steps. This leads to the appearance of Chebyshev polynomials of the third and fourth kind in Bailey pairs related to Bailey's Lemma. The natural relationship with L.J. Rogers's pioneering work is also presented.
引用
收藏
页码：443 / 464
页数：22
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