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

  • George E. AndrewsEmail author


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.


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

Mathematics Subject Classification

05A17 05A19 11P83 



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Authors and Affiliations

  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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