# Second Order Mock Theta Functions

@article{McIntosh2007SecondOM, title={Second Order Mock Theta Functions}, author={Richard J. McIntosh}, journal={Canadian Mathematical Bulletin}, year={2007}, volume={50}, pages={284 - 290} }

Abstract In his last letter to Hardy, Ramanujan defined 17 functions $F\left( q \right)$ , where $\left| q \right|<1$ . He called them mock theta functions, because as $q$ radially approaches any point ${{e}^{2\pi ir}}\left( r\,\text{rational} \right)$ , there is a theta function ${{F}_{r}}\left( q \right)$ with $F\left( q \right)-{{F}_{r}}\left( q \right)=O\left( 1 \right)$ . In this paper we establish the relationship between two families of mock theta functions.

## 57 Citations

### The H and K Family of Mock Theta Functions

- MathematicsCanadian Journal of Mathematics
- 2012

Abstract In his last letter to Hardy, Ramanujan defined 17 functions $F\left( q \right),\,\left| q \right|\,<\,1$ , which he called mock $\theta $ -functions. He observed that as $q$ radially…

### The Mordell integral, quantum modular forms, and mock Jacobi forms

- Mathematics
- 2015

AbstractIt is explained how the Mordell integral ∫Reπiτx2−2πzxcosh(πx)dx
$$\int_{\mathbb R} \frac{e^{\pi i \tau x^{2} - 2\pi zx}}{\cosh(\pi x)} dx $$
unifies the mock theta functions, partial…

### Some identities for Appell–Lerch sums and a universal mock theta function

- Mathematics
- 2018

In their paper “A survey of classical mock theta functions”, Gordon and McIntosh observed that the classical mock $$\theta $$θ-functions, including those found by Ramanujan, can be expressed in terms…

### A Survey of Classical Mock Theta Functions

- Mathematics
- 2012

In his last letter to Hardy, Ramanujan defined 17 functions M(q), | q | < 1, which he called mock θ-functions. He observed that as q radially approaches any root of unity ζ at which M(q) has an…

### On second and eighth order mock theta functions

- MathematicsThe Ramanujan Journal
- 2018

Mock theta functions have been deeply studied in the literature. Historically, there are many forms of representations for mock theta functions: Eulerian forms, Hecke-type double sums, Appell–Lerch…

### Bilateral series in terms of mixed mock modular forms

- Mathematics
- 2016

The number of strongly unimodal sequences of weight n is denoted by u∗(n)$u^{*}(n)$. The generating functions for {u∗(n)}n=1∞$\{u^{*}(n)\}_{n=1}^{\infty}$ are…

### New mock theta conjectures Part I

- Mathematics
- 2018

In their paper “A survey of classical mock theta functions”, Gordon and McIntosh observed that the classical mock $$\theta $$θ-functions, including those found by Ramanujan, can be expressed in terms…

### Completions and algebraic formulas for the coefficients of Ramanujan’s mock theta functions

- Materials ScienceThe Ramanujan Journal
- 2020

We present completions of mock theta functions to harmonic weak Maass forms of weight \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

### ON PARTIAL SUMS OF MOCK THETA FUNCTIONS OF ORDER 2

- Mathematics
- 2013

In his last letter to Hardy, Ramanujan defined 17 f unctions F(q), where | q | < 1. He called them moc k theta functions, because as q radially approaches any poi nt Γ Πi e 2 (r rational), there is a…

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