Some Eighth Order Mock Theta Functions

2000/10/01 by Basil Gordon, Richard J. McIntosh, Richard J. Mcintosh · 6 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematical functions and polynomials

paper · doi:10.1112/s0024610700008735

Abstract

A method is developed for obtaining Ramanujan's mock theta functions from ordinary theta functions by performing certain operations on their q-series expansions. The method is then used to construct several new mock theta functions, including the first ones of eighth order. Summation and transformation formulae for basic hypergeometric series are used to prove that the new functions actually have the mock theta property. The modular transformation formulae for these functions are obtained.

Cited by

• Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
• Some new mock theta functions
• Bilateral Two-Parameter Mock Theta Functions and Related Applications
• Generating Functions of the Hurwitz Class Numbers Associated with Certain Mock Theta Functions
• Asymptotic formulae for Eulerian series
• Completions and algebraic formulas for the coefficients of Ramanujan's mock theta functions. [europepmc]

Related

• Modular Transformations of Ramanujan's Tenth Order Mock Theta Functions
• Second Order Mock Theta Functions
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• Transformation of Third Order Mock Theta Functions and New q-Series Identities
• Short proofs of Ramanujan-like identities for the eighth order mock theta function V₀(q)