Rogers-Ramanujan-Slater Type Identities

Laughlin, James Mc; Sills, Andrew V.; Zimmer, Peter

doi:10.37236/36

Cited by 27 publications

(15 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…[29] and [30] and used them to prove a massive list of Roger-Ramanujan type identites. Rather than say too much of their history, recent developments, and applications, we refer the reader to Chapter 3 of [4] and the survey articles [5,24,31]. aq; q 2 n q n β n = 1 (aq 2 ; q 2 ) ∞ (q; q) ∞ r,n≥0 (−a) n q n 2 +2rn+r+n α r ,…”

Section: Preliminaries and Statement Of Resultsmentioning

confidence: 99%

Some Smallest Parts Functions from Variations of Bailey’s Lemma

Jennings-Shaffer¹

2018

Frontiers in Orthogonal Polynomials and q-Series

View full text Add to dashboard Cite

We construct new smallest parts partition functions and smallest parts crank functions by considering variations of Bailey's Lemma and conjugate Bailey pairs. The functions we introduce satisfy simple linear congruences modulo 3 and 5. We introduce and give identities for two four variable q-hypergeometric functions; these functions specialize to some of our new spt-crank-type functions as well as many known spt-crank-type functions.

show abstract

Section: Preliminaries and Statement Of Resultsmentioning

confidence: 99%

Some Smallest Parts Functions from Variations of Bailey’s Lemma

Jennings-Shaffer¹

2018

Frontiers in Orthogonal Polynomials and q-Series

View full text Add to dashboard Cite

show abstract

“…More precisely, (2.6a) is obtained by setting ρ 1 , ρ 2 → ∞, (2.6b) is derived by taking q → q 2 , ρ 1 → ∞, ρ 2 → −q, (2.6c) is followed by setting ρ 1 → √ q, ρ 2 → − √ q, and (2.6d) is derived by taking ρ 1 → ∞, ρ 2 → −1. For more details, see, for example, [16,20,30]. Moreover, by applying Bailey's lemma iteratively to an appropriate Bailey pair in the simple sum case, one can obtain multi-analog identities of Rogers-Ramanujan type straightforwardly.…”

Section: Chebyshev Polynomials and Bailey's Lemmamentioning

confidence: 99%

“…For these identities, one can see that (5.2a) is contained in Slater's list [32, (4)] with q → −q and also can be found in [20 (5.2d) is Entry 5.3.9 in [10, P. 105]. Specially, (5.2e) seems to be new, which can be seen as a missing member of modular 4 identities in Slater's list, see [32, P. 153] and [20, P. 11].…”

Section: The Weak Forms (26b) and (26c) Of Bailey's Lemmamentioning

confidence: 99%

Rogers-Ramanujan type identities and Chebyshev Polynomials of the third kind

Sun¹

2021

Preprint

View full text Add to dashboard Cite

It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. During studying Dyson's "favorite" identity of Rogers-Ramanujan type, Andrews pointed out that the classical orthogonal polynomials also have surprising applications in the world of q. By inserting Chebyshev polynomials of the third and the fourth kinds into Bailey pairs, Andrews derived a family of Rogers-Ramanujan type identities and also results related to mock theta functions and Hecke-type series. In this paper, by constructing a new Bailey pair involving Chebyshev polynomials of the third kind, we further extend Andrews' way in the studying of Rogers-Ramanujan type identities. By fitting this Bailey pair into different weak forms of Bailey's lemma, we obtain a companion identity to Dyson's favorite one and also many other Rogers-Ramanujan type identities. Furthermore, as immediate consequences, we also obtain some results related to Appell-Lerch series and the generalized Hecke-type series.

show abstract

“…which is (S.83) in [13]. In view of (1.1) and (1.3), the authors in [2] posed the following (slightly rewritten) problem.…”

Section: Introductionmentioning

confidence: 99%