Rogers–Ramanujan type identities and Chebyshev polynomials of the third kind

It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. While studying Dyson’s “favorite” identity Rogers–Ramanujan type, Andrews pointed out classical orthogonal also have surprising applications world q. By introducing Chebyshev third fourth kinds into Bailey pairs, derived a family type identities results related to mock theta functions Hecke-type series. In this paper, by constructing new pair involving kind, we further extend Andrews’ way Rogers-Ramanujan identities. inserting various weak forms Bailey’s lemma, obtain companion for favorite number As consequences, Appell–Lerch series generalized Furthermore, our key fits bilateral versions lemma due Warnaar, which leads more false