Second Order Mock Theta Functions

2007/06/01 by Richard J. McIntosh · 4 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematical functions and polynomials

paper · pdf · doi:10.4153/cmb-2007-028-9

Abstract

Abstract In his last letter to Hardy, Ramanujan defined 17 functions F ( q ), where | q | < 1. He called them mock theta functions, because as q radially approaches any point e 2 πir ( r rational), there is a theta function F r ( q ) with F ( q ) − Fr ( q ) = O (1). In this paper we establish the relationship between two families of mock theta functions.

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• 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
• Infinite families of congruences for the second order mock theta function B(q)

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