Tenth order mock theta functions in Ramanujan's lost notebook (IV)
Author:
YounSeo Choi
Journal:
Trans. Amer. Math. Soc. 354 (2002), 705733
MSC (2000):
Primary 11B65; Secondary 11F20, 33E05
Published electronically:
September 21, 2001
MathSciNet review:
1862564
Fulltext PDF Free Access
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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
YounSeo Choi
Affiliation:
Department of Mathematics, Korea University, 51, Anamdong, Sungbukku, Seoul, 136701, Korea
Email:
ychoi2@mail.korea.ac.kr
DOI:
http://dx.doi.org/10.1090/S0002994701028616
PII:
S 00029947(01)028616
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
