Tenth order mock theta functions in Ramanujan's lost notebook III

@article{Choi2007TenthOM,
  title={Tenth order mock theta functions in Ramanujan's lost notebook III},
  author={Youn-Seo Choi},
  journal={Proceedings of the London Mathematical Society},
  year={2007},
  volume={94}
}
  • Youn-Seo Choi
  • Published 1 January 2007
  • Mathematics
  • Proceedings of the London Mathematical Society
Ramanujan's lost notebook contains many results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions. Previously, the author proved six of the eight tenth order mock theta function identities. It is the purpose of this paper to prove the fifth and sixth identities of Ramanujan's tenth order mock theta functions. The properties of modular forms are used for the proofs of theta function identities. 
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References

SHOWING 1-10 OF 16 REFERENCES
Tenth order mock theta functions in Ramanujan's Lost Notebook
Ramanujan's lost notebook contains many results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions. Previously the author proved
Tenth order mock theta functions in Ramanujan’s lost notebook (IV)
Ramanujan's lost notebook contains many results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions. Previously the author proved
Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook II
In S. Ramanujan's last letter to G. H. Hardy [B4], Ramanujan proclaimed, ``I discovered very interesting functions recently which I call `Mock' -functions.'' He then provided a long list of ``third
On the seventh order mock theta functions
In a recent paper [H], we proved the "Mock Theta Conjectures". These are identities, stated by Ramanujan in his "lost notebook" JR2, pp. 19-20], involving two of the 5th order mock 0-functions. In
The lost notebook and other unpublished papers
Modular Functions In Analytic Number Theory
Knopp's engaging book presents an introduction to modular functions in number theory by concentrating on two modular functions, $\eta(\tau)$ and $\vartheta(\tau)$, and their applications to two
the sixth order mock theta functions’, Adv
  • Math. 89
  • 1991
A proof of the mock theta conjectures
Ramanujan: Letters and Commentary
A brief biography of Ramanujan Ramanujan in Madras (chapter 1) Ramanujan's first two letters to Hardy and Hardy's response (chapter 2) Preparing to go to England (chapter 3) Ramanujan at Cambridge
...
...