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

2007 ◽  
Vol 44 (4) ◽  
pp. 767-777 ◽  
Author(s):  
Bhaskar Srivastava
Keyword(s):  
Theta Functions ◽  
Padé Approximants ◽  
Second Order ◽  
Mock Theta Functions ◽  
Pade Approximants

ON SOME NEW MOCK THETA FUNCTIONS

2018 ◽  
Vol 107 (1) ◽  
pp. 53-66
Author(s):  
NANCY S. S. GU ◽  
LI-JUN HAO
Keyword(s):  
Theta Functions ◽  
Constant Term ◽  
Second Order ◽  
Sixth Order ◽  
Mock Theta Functions ◽  
Dual Nature ◽  
Partial 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 how this pair gives rise to new mock theta functions in terms of Appell–Lerch sums. Furthermore, we establish some relations between these new mock theta functions and some second-order mock theta functions. Meanwhile, we obtain an identity between a second-order and a sixth-order mock theta functions. In addition, we provide the mock theta conjectures for these new mock theta functions. Finally, we discuss the dual nature between the new mock theta functions and partial theta functions.

Combinatorics of two second-order mock theta functions

2020 ◽  
pp. 1-11
Author(s):  
Hannah Burson
Keyword(s):  
Theta Function ◽  
Theta Functions ◽  
Second Order ◽  
Mock Theta Function ◽  
Mock Theta Functions ◽  
Third Order ◽  
Combinatorial Interpretations ◽  
Special Cases ◽  
Order Mock Theta Function

We introduce combinatorial interpretations of the coefficients of two second-order mock theta functions. Then, we provide a bijection that relates the two combinatorial interpretations for each function. By studying other special cases of the multivariate identity proved by the bijection, we obtain new combinatorial interpretations for the coefficients of Watson’s third-order mock theta function [Formula: see text] and Ramanujan’s third-order mock theta function [Formula: see text].

Second Order Mock Theta Functions

2007 ◽  
Vol 50 (2) ◽  
pp. 284-290 ◽  
Author(s):  
Richard J. McIntosh
Keyword(s):  
Theta Function ◽  
Theta Functions ◽  
Second Order ◽  
Mock Theta Functions ◽  
The Relationship

AbstractIn his last letter to Hardy, Ramanujan defined 17 functions F(q), where |q| < 1. He called them mock theta functions, because as q radially approaches any point e2πir (r rational), there is a theta function Fr(q) with F(q) − Fr(q) = O(1). In this paper we establish the relationship between two families of mock theta functions.

On finite forms of Bailey's 2ψ2 transformation formulae and their applications

2016 ◽  
Vol 12 (08) ◽  
pp. 2189-2200
Author(s):  
A. Bayad ◽  
D. D. Somashekara ◽  
K. Narasimha Murthy
Keyword(s):  
Simple Proof ◽  
Theta Functions ◽  
Second Order ◽  
Mock Theta Functions

In this paper, we study finite forms of Bailey's transformation formulae and therefrom, we deduce the Bailey's transformation formulae. Further, we derive finite forms of the complete mock theta functions of second order. Also we give a simple proof of one of Bailey's transformation formulae and present some applications.

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