The Bailey transform and Hecke-Rogers identities for the universal mock\n theta functions

2014/06/17 by Kathy Q. Ji, Ji, Kathy Q., Aviva X. H. Zhao +1
Chemistry · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1406.4398

openalex publication_date 2014/06/17 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Recently, Garvan obtained two-variable Hecke-Rogers identities for three\nuniversal mock theta functions g₂(z;q), ,g₃(z;q), ,K(z;q) by using basic\nhypergeometric functions, and he proposed a problem of finding direct proofs of\nthese identities by using Bailey pair technology. In this paper, we give proofs\nof Garvan's identities by applying Bailey's transform with the conjugate Bailey\npair of Warnaar and three Bailey pairs deduced from two special cases of\n₆\ψ₆ given by Slater. In particular, we obtain a compact form of\ntwo-variable Hecke-Rogers identity related to g₃(z;q), which imply the\ncorresponding identity given by Garvan. We also extend these two-variable\nHecke-Rogers identities into infinite families.\n

Citations

• The H and K Family of Mock Theta Functions

Related

• Universal mock theta functions and two-variable Hecke-Rogers identities
• Further results on Andrews--Yee's two identities for mock theta functions ω(z;q) and v(z;q)
• Bailey Type Transforms and Applications
• Rogers-Ramanujan type identities and Chebyshev Polynomials of the third kind
• New fifth and seventh order mock theta function identities