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

Author:
Youn-Seo Choi

Journal:
Trans. Amer. Math. Soc. **354** (2002), 705-733

MSC (2000):
Primary 11B65; Secondary 11F20, 33E05

DOI:
https://doi.org/10.1090/S0002-9947-01-02861-6

Published electronically:
September 21, 2001

MathSciNet review:
1862564

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Abstract: 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 transformation formula for the definite integral plays a key role in the proofs of these identities. Also, the properties of modular forms are used for the proofs of theta function identities.

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Additional Information

**Youn-Seo Choi**

Affiliation:
Department of Mathematics, Korea University, 5-1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Korea

Email:
y-choi2@mail.korea.ac.kr

DOI:
https://doi.org/10.1090/S0002-9947-01-02861-6

Keywords:
Ramanujan,
definite integral,
theta function,
mock theta function

Received by editor(s):
August 11, 2000

Published electronically:
September 21, 2001

Article copyright:
© Copyright 2001
American Mathematical Society