# Representations of mock theta functions

@article{Chen2020RepresentationsOM, title={Representations of mock theta functions}, author={Dandan Chen and Liuquan Wang}, journal={Advances in Mathematics}, year={2020} }

Motivated by the works of Liu, we provide a unified approach to find Appell-Lerch series and Hecke-type series representations for mock theta functions. We establish a number of parameterized identities with two parameters $a$ and $b$. Specializing the choices of $(a,b)$, we not only give various known and new representations for the mock theta functions of orders 2, 3, 5, 6 and 8, but also present many other interesting identities. We find that some mock theta functions of different orders are…

## 8 Citations

### ON SOME NEW MOCK THETA FUNCTIONS

- MathematicsJournal of the Australian Mathematical Society
- 2018

In 1991, Andrews and Hickerson established a new Bailey pair and combined it with the constant term method to prove some results related to sixth-order mock theta functions. In this paper, we study…

### Hecke–Rogers type series representations for infinite products

- MathematicsThe Ramanujan Journal
- 2021

In this paper, we give a new proof of Liu’s extension of the non-terminating $$_6\phi _5$$
summation formula. Based on this formula, some Hecke–Rogers type series representations for infinite…

### Some further Hecke-type identities

- MathematicsInternational Journal of Number Theory
- 2020

In this paper, we obtain some Hecke-type identities by using two [Formula: see text]-series expansion formulae. And, the identities can also be proved directly in terms of Bailey pairs. In…

### New families of mock theta functions and partial fraction decomposition

- MathematicsAdv. Appl. Math.
- 2022

### Infinite families of Hecke-Rogers type series and their truncated representations

- MathematicsAdv. Appl. Math.
- 2022

### Expansion formulas for multiple basic hypergeometric series over root systems

- MathematicsAdv. Appl. Math.
- 2022

## References

SHOWING 1-10 OF 51 REFERENCES

### 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…

### Mock Theta Functions

- Mathematics
- 2008

The mock theta functions were invented by the Indian mathematician Srinivasa Ramanujan, who lived from 1887 until 1920. He discovered them shortly before his death. In this dissertation, I consider…

### 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 the seventh order mock theta functions

- Mathematics
- 1988

In a recent paper [H], we proved the "Mock Theta Conjectures". These are identities, stated by Ramanujan in his "lost notebook" JR2, pp. 19-20], involving two of the 5th order mock 0-functions. In…

### Hecke‐type double sums, Appell–Lerch sums, and mock theta functions, I

- Mathematics
- 2014

By introducing a dual notion between partial theta functions and Appell–Lerch sums, we find and prove a formula which expresses Hecke‐type double sums in terms of Appell–Lerch sums. Not only does our…

### Automatic Proof of Theta-Function Identities

- MathematicsTexts & Monographs in Symbolic Computation
- 2019

This is a tutorial for using two new MAPLE packages, thetaids and ramarobinsids. The thetaids package is designed for proving generalized eta-product identities using the valence formula for modular…

### 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…

### Universal mock theta functions and two-variable Hecke–Rogers identities

- Mathematics
- 2014

We obtain two-variable Hecke–Rogers identities for three universal mock theta functions. This implies that many of Ramanujan’s mock theta functions, including all the third-order functions, have a…

### On three third order mock theta functions and Hecke-type double sums

- Mathematics
- 2013

We obtain four Hecke-type double sums for three of Ramanujan’s third order mock theta functions. We discuss how these four are related to the new mock theta functions of Andrews’ work on q-orthogonal…