Vanishing coefficients in several q-series expansions related to the Rogers--Ramanujan continued fraction

2020/03/28 by Shane Chern, Chern, Shane, Dazhao Tang +1
Mathematics · #11F27 #30B10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2003.12707

openalex publication_date 2020/03/28 · openalex created_date 2020/04/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate several infinite products with vanishing Taylor coefficients in arihmetic progressions. These infinite products are closely related to the Rogers--Ramanujan continued fraction. Moreover, a handful of new identities involving Ramanujan's parameters will be established.

Citations

• Some Observations on Lambert series, vanishing coefficients and dissections of infinite products and series

Related

• Some Observations on Lambert series, vanishing coefficients and dissections of infinite products and series
• The Rogers--Ramanujan continued fraction
• Sign Patterns and Congruences of certain infinite products involving the Rogers-Ramanujan continued fraction
• Ramanujan's q-continued fractions
• Some identities of Ramanujan's q-Continued Fraction of Order Eighteen, Twenty-Six and Thirty, and Vanishing Coefficients