On second and eighth order mock theta functions

@article{Cui2018OnSA,
  title={On second and eighth order mock theta functions},
  author={Su-Ping Cui and Nancy S. S. Gu and Li-jun Hao},
  journal={The Ramanujan Journal},
  year={2018},
  pages={1-30}
}
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 sums, and Fourier coefficients of meromorphic Jacobi forms. In this paper, we first establish Hecke-type double sums for the second and eighth order mock theta functions by Bailey’s lemma and a Bailey pair given by Andrews and Hickerson. Meanwhile, we give different proofs of the generalized Lambert… 

Representations of mock theta functions

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

Parity of coefficients of mock theta functions

ON SOME NEW MOCK THETA FUNCTIONS

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

References

SHOWING 1-10 OF 19 REFERENCES

New mock theta conjectures Part I

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

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

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

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

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

Some Eighth Order Mock Theta Functions

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

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

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

Tenth order mock theta functions in Ramanujan's Lost Notebook

Ramanujan's lost notebook contains many results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions. Previously, the author proved

The fifth and seventh order mock theta functions

. The theory of Bailey chains is extended to yield identities for Hecke type modular forms and related generalizations. The extended results allow us to produce Hecke type series for the fifth and

Second Order Mock Theta Functions

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

q-Orthogonal polynomials, Rogers-Ramanujan identities, and mock theta functions

In this paper, we examine the role that q-orthogonal polynomials can play in the application of Bailey pairs. The use of specializations of q-orthogonal polynomials reveals new instances of mock