Dyson’s “Favorite” Identity and Chebyshev Polynomials of the Third and Fourth Kind

George E. Andrews

doi:10.1007/s00026-019-00443-w

Dyson’s “Favorite” Identity and Chebyshev Polynomials of the Third and Fourth Kind

George E. Andrews

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	443-464
Number of pages	22
Journal	Annals of Combinatorics
Volume	23
Issue number	3-4
DOIs	https://doi.org/10.1007/s00026-019-00443-w
State	Published - Nov 1 2019

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1007/s00026-019-00443-w

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Dyson’s “Favorite” Identity and Chebyshev Polynomials of the Third and Fourth Kind

Abstract

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