Vol. 10, No. 5, 2017

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A solution to a problem of Frechette and Locus

Chenthuran Abeyakaran

Vol. 10 (2017), No. 5, 893–900

In a recent paper, Frechette and Locus examined and found expressions for the infinite product Dm(q) := t=1(1 qmt)(1 qt) in terms of products of q-series of the Rogers–Ramanujan type coming from Hall–Littlewood polynomials, when m 0,1,2(mod4). These q-series were originally discovered in 2014 by Griffin, Ono, and Warnaar in their work on the framework of the Rogers–Ramanujan identities. Extending this framework, Rains and Warnaar also recently discovered more q-series and their corresponding infinite products. Frechette and Locus left open the case where m 3(mod4). Here we find such an expression for the infinite products for m 3(mod4) by making use of the new q-series obtained by Rains and Warnaar.

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Rogers–Ramanujan Identities
Mathematical Subject Classification 2010
Primary: 11P84
Received: 29 July 2016
Revised: 18 August 2016
Accepted: 21 August 2016
Published: 14 May 2017

Communicated by Ken Ono
Chenthuran Abeyakaran
Chamblee Charter High School
3688 Chamblee Dunwoody Rd
Chamblee, GA 30341
United States