On Cranks of Partitions, Generalized Lambert Series, and Basic Hypergeometric Series
Chan, Song Heng
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https://hdl.handle.net/2142/86850
Description
Title
On Cranks of Partitions, Generalized Lambert Series, and Basic Hypergeometric Series
Author(s)
Chan, Song Heng
Issue Date
2005
Doctoral Committee Chair(s)
Berndt, Bruce C.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
In Chapters 4 and 5, we apply the same method used in Chapter 3 on basic hypergeometric series. In Chapter 4, we present a new proof of Ramanujan's 10, summation formula. And finally, in Chapter 5, we present a new proof of a general transformation formula for basic hypergeometric series that was discovered by D. B. Sears in 1951. We also discuss some special cases.
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