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

  • George E. AndrewsEmail author
Article
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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.

Keywords

Partitions Dyson’s favorite identity Bailey pairs Bailey’s lemma Partitions Chebyshev polynomials Mock theta functions 

Mathematics Subject Classification

05A17 05A19 11P83 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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