Results 131 to 140 of about 44,715 (186)

Second Order Mock Theta Functions

Canadian Mathematical Bulletin, 2007
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.
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Quantum q-series and mock theta functions

Research in the Mathematical Sciences
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Folsom, Amanda, Metacarpa, David
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Congruences for the coefficients of the Gordon and McIntosh mock theta function ξ(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \beg

The Ramanujan journal, 2021
Recently Gordon and McIntosh introduced the third order mock theta function $\xi(q)$ defined by $$ \xi(q)=1+2\sum_{n=1}^{\infty}\frac{q^{6n^2-6n+1}}{(q;q^6)_{n}(q^5;q^6)_{n}}.
R. Silva, James A. Sellers
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New congruences modulo 9 for the coefficients of Gordon-McIntosh's mock theta function ξ(q)

Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2023
In recent years, congruence properties for the coefficients of mock theta functions have been studied by mathematicians. Recently, Silva and Sellers proved some congruences modulo 3 and 9 for the coefficients of the third order mock theta function ξ(q ...
O. Yao
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Short proofs of Ramanujan-like identities for the eighth order mock theta function V0(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}

The Ramanujan journal, 2023
Using Appell function properties we give short proofs of Ramanujan-like identities for the eighth order mock theta function V0(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb ...
Eric T. Mortenson
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Identities involving mock theta functions and theta functions

Proceedings of the American Mathematical Society, 2023
In this paper, we first present new representations for several mock theta functions. In view of the sign flips on these identities, some interesting results involving theta functions are established by new Bailey pairs and Watson’s 8 ϕ 7 _8\phi _7 transformation ...
Song, Hanfei, Wang, Chun
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Some Eighth Order Mock Theta Functions

Journal of the London Mathematical Society, 2000
Summary: 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.
Gordon, Basil, McIntosh, Richard J.
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OVERPARTITIONS RELATED TO THE MOCK THETA FUNCTION

, 2020
Recently, Brietzke, Silva and Sellers [‘Congruences related to an eighth order mock theta function of Gordon and McIntosh’, J. Math. Anal. Appl.479 (2019), 62–89] studied the number $v_{0}(n)$ of overpartitions of $n$ into odd parts without gaps between ...
Bernard L. S. Lin
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A mock theta function identity related to the partition rank modulo 3 and 9

, 2020
We prove a new mock theta function identity related to the partition rank modulo 3 and 9. As a consequence, we obtain the [Formula: see text]-dissection of the rank generating function modulo [Formula: see text]. We also evaluate all of the components of
Song Heng Chan, Nankun Hong, Jerry, Jeremy Lovejoy   +3 more
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ON SOME NEW MOCK THETA FUNCTIONS

Journal 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 how this pair gives rise to new mock theta functions in terms of Appell–Lerch sums.
NANCY S. S. GU, LI-JUN HAO
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