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 language||English (US)|
|Title of host publication||Trends in Mathematics|
|Publisher||Springer Science and Business Media Deutschland GmbH|
|Number of pages||22|
|State||Published - 2021|
|Name||Trends in Mathematics|
All Science Journal Classification (ASJC) codes