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
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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
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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
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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 knobExpand
Several new product identities in relation to two-variable Rogers-Ramanujan type sums and mock theta functions
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Ramanujan's "Lost" Notebook VI: The Mock Theta Conjectures
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
  • Bin Chen
  • Mathematics, Medicine
  • Journal of inequalities and applications
  • 2018
TLDR
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
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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
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
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
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-RademacherExpand
Generalized hypergeometric functions
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 SeriesExpand
MULTIPLE SERIES ROGERS-RAMANUJAN TYPE IDENTITIES
On montre comment chacune des identites classiques du type Rogers-Ramanujan peut se plonger dans une famille infinie d'identites serie multiple
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