# The fifth and seventh order mock theta functions

@article{Andrews1986TheFA,
title={The fifth and seventh order mock theta functions},
author={G. Andrews},
journal={Transactions of the American Mathematical Society},
year={1986},
volume={293},
pages={113-134}
}
• G. Andrews
• Published 1986
• Mathematics
• Transactions of the American Mathematical Society
146 Citations
On the dual nature theory of bilateral series associated to mock theta functions
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 dualExpand
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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–LerchExpand
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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 ofExpand
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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 considerExpand
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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 parameterizedExpand
Your hit parade: The top ten most fascinating formulas in Ramanujan's lost notebook
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Several new product identities in relation to two-variable Rogers-Ramanujan type sums and mock theta functions
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
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• Bin Chen
• 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) $\omega(q). Expand #### References SHOWING 1-10 OF 16 REFERENCES An Introduction to Ramanujan's “Lost” Notebook In the spring of 1976, the first author visited Trinity College Library at Cambridge University. Dr. Lucy Slater had suggested to him that there were materials deposited there from the estate of theExpand Hecke modular forms and$q\$-hermite polynomials
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