#### 146 Citations

On the dual nature theory of bilateral series associated to mock theta functions

- Mathematics
- 2018

In recent work, Hickerson and Mortenson introduced a dual notion between Appell–Lerch sums and partial theta functions. In this sense, Appell–Lerch sums and partial theta functions appear to be dual… Expand

On second and eighth order mock theta functions

- Mathematics
- 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… Expand

Representations of mock theta functions

- Mathematics
- 2020

Abstract 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… Expand

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… Expand

Several new product identities in relation to Rogers–Ramanujan type sums and mock theta functions

- 2021

Product identities in two variables x , q expand infinite products as infinite sums, which are linear combinations of theta functions; famous examples include Jacobi’s triple product identity,… Expand

Representations of mock theta functions

- Mathematics
- 2018

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… Expand

Your hit parade: The top ten most fascinating formulas in Ramanujan's lost notebook

- Mathematics
- 2008

A t 7:30 on a Saturday evening in March 1956, the first author sat down in an easy chair in the living room of his parents’ farm home ten miles east of Salem, Oregon, and turned the TV channel knob… Expand

Several new product identities in relation to two-variable Rogers-Ramanujan type sums and mock theta functions

- Mathematics
- 2020

Product identities in two variables $x, q$ expand infinite products as infinite sums, which are linear combinations of theta functions; famous examples include Jacobi's triple product identity,… Expand

Ramanujan's "Lost" Notebook VI: The Mock Theta Conjectures

- Mathematics
- 1989

1. INTRODUCTION In this paper we shall consider only Ramanujan’s two families of fifth- order mock theta functions. These functions were briefly described in Ramanujan’s last letter to G. H. Hardy [… Expand

Mock theta functions and Appell–Lerch sums

- Mathematics, Medicine
- Journal of inequalities and applications
- 2018

The bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums is presented and a very interesting congruence relationship of the bilateral series B(ω;q)$B(\omega;q).$ for the third order Mock theta function ω(q) $\omega(q). Expand

#### References

SHOWING 1-10 OF 16 REFERENCES

An Introduction to Ramanujan's “Lost” Notebook

- Mathematics
- 1979

In the spring of 1976, the first author visited Trinity College Library at Cambridge University. Dr. Lucy Slater had suggested to him that there were materials deposited there from the estate of the… Expand

Hecke modular forms and $q$-hermite polynomials

- Mathematics
- 1986

A l'aide de la technique de developpement en termes de q-polynomes d'Hermite A n (cosθ/q)=Σ i =0,...,n[n,i]cos(n-2i)θ, ou [n,i]=Πj=1,...,i (1-q n-ii+j )/(1-q j ) est le polynome de Frauss (cf L. J.… Expand

A SHORT PROOF OF AN IDENTITY OF EULER

- Mathematics
- 1951

Further v? can, apart from trivial (unit) factors, be expressed in at most one way as a product of indecomposable factors. The same results hold for families of regular bilinear mappings (n = 2, H =… Expand

The theory of partitions

- Mathematics
- 1976

1. The elementary theory of partitions 2. Infinite series generating functions 3. Restricted partitions and permutations 4. Compositions and Simon Newcomb's problem 5. The Hardy-Ramanujan-Rademacher… Expand

Generalized hypergeometric functions

- Mathematics, Physics
- 1966

1. The Gauss Function 2. The Generalized Gauss Function 3. Basic Hypergeometric Functions 4. Hypergeometric Integrals 5. Basic Hypergeometric Integrals 6. Bilateral Series 7. Basic Bilateral Series… Expand

MULTIPLE SERIES ROGERS-RAMANUJAN TYPE IDENTITIES

- Mathematics
- 1984

On montre comment chacune des identites classiques du type Rogers-Ramanujan peut se plonger dans une famille infinie d'identites serie multiple