# Some Eighth Order Mock Theta Functions

@article{Gordon2000SomeEO, title={Some Eighth Order Mock Theta Functions}, author={Basil Gordon and Richard J. McIntosh}, journal={Journal of the London Mathematical Society}, year={2000}, volume={62} }

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 several new mock theta functions, including the first ones of eighth order. Summation and transformation formulae for basic hypergeometric series are used to prove that the new functions actually have the mock theta property. The modular transformation formulae for these functions are obtained.

## 92 Citations

PARTIAL SECOND ORDER MOCK THETA FUNCTIONS, THEIR EXPANSIONS AND PADE APPROXIMANTS

- Mathematics
- 2007

By proving a summation formula, we enumerate the expansions for the mock theta functions of order 2 in terms of partial mock theta functions of order 2, 3 and 6. We show a relation between…

ON GENERALIZED EIGHTH ORDER MOCK THETA FUNCTIONS

- Mathematics
- 2020

In this paper we have generalized eighth order mock theta functions, recently introduced by Gordon and MacIntosh involving four independent variables. The idea of generalizing was to have four extra…

Relations Connecting Eighth Order Mock Theta Functions

- Mathematics
- 2013

Du ring the last years of his life, Ramanujan defined 17 functions F(q), where | q | < 1, and he named them as mock theta functions. The first detailed description of mock theta functions was given…

Bilateral Generalization of Fifth and Eighth Order Mock Theta Functions

- Mathematics
- 2013

We generalize fifth order mock theta functions of Ramanujan and eighth order mock theta functions of Gordon and McIntosh. We show they are �� ��-functions and give their alternative definition. We…

A Note on Certain Properties of Mock Theta Functions of Order Eight

- Mathematics
- 2014

In this paper, we have developed a non-homogeneous q- difierence equa- tion of flrst order for the generalized Mock theta function of order eight and besides these established limiting case of Mock…

Two-Variable Generalization of New Mock Theta Functions

- Mathematics
- 2013

We define two variable generalization of new mock theta functions recently developed by Andrews and also of two new mock theta functions developed by Bringmann et al and give functional equations…

A Note on Continued Fractions and Mock Theta Functions

- Mathematics
- 2016

Mock theta functions are the most interesting topic mentioned in Ramanujan’s Lost Notebook, due to its emerging application in the field of Number theory, Quantum invariants theory and etc. In the…

Some Relations on Sixth Order Mock Theta Functions

- Mathematics
- 2013

During the last years of his life, Ramanujan defined 17 functions F(q), where | q | < 1. Ramanujan named them as mock theta functions, because as q radially approaches any point e 2∏iΓ (r rational),…

ON FOUR NEW MOCK THETA FUNCTIONS

- Mathematics
- 2020

In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and…

A COMPREHENSIVE STUDY OF SECOND ORDER MOCK THETA FUNCTIONS

- Mathematics
- 2005

We consider the second order mock theta functions de- flned by McIntosh and deflne generalized functions. We give integral representation and multibasic expansion of these functions. We also show…

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