# Tenth order mock theta functions in Ramanujan's Lost Notebook

@article{Choi1999TenthOM, title={Tenth order mock theta functions in Ramanujan's Lost Notebook}, author={Youn-Seo Choi}, journal={Inventiones mathematicae}, year={1999}, volume={136}, pages={497-569} }

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 the first six of Ramanujan's tenth order mock theta function identities. It is the purpose of this paper to prove the seventh and eighth identities of Ramanujan's tenth order mock theta function identities which are expressed by mock theta functions and a definite integral. L. J. Mordell's…

## 92 Citations

Tenth order mock theta functions in Ramanujan’s lost notebook (IV)

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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 III

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Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook II

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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…

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In this paper we have given 3 independent variable generalization of tenth order mock theta functions and have found some relations between generalized mock theta functions of different order. We…

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A generalization of Ramanujan’s fifth order and tenth order mock theta functions is given. It is shown that these belong to the family of Fq-functions. Using the properties of Fq-functions,…

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The modular transformations of Ramanujan's tenth order mock theta functions are computed, beginning from Choi's Hecke-type identites and using Zwegers' results on indefinite theta series. Explicit…

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- MathematicsThe Ramanujan Journal
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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–Lerch…

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In his “lost notebook” (p. 202 of the 1988 edition), S. Ramanujan recorded modular transformations involving the Mordell integral, q-hypergeometric series, and generalized Lambert series. He gave no…

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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 consider…

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