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

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The combinatorial and analytic properties of Dyson’s “favorite” identity are studied in detail. In particular, a q-series analog of the antitelescoping 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 languageEnglish (US)
Title of host publicationTrends in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Pages89-110
Number of pages22
DOIs
StatePublished - 2021

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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