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On the difference of partial theta funct...
Berkovich, Alexander...

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On the difference of partial theta functions by Berkovich, Alexander ( Author )
Lemonjar Open Access
Australian National University
01-08-2023
Sums of the form add((-1)^n q^(n(n-1)/2) x^n, n>=0) are called partial theta functions. In his lost notebook, Ramanujan recorded many identities for those functions. In 2003, Warnaar found an elegant formula for a sum of two partial theta functions. Subsequently, Andrews and Warnaar established a similar result for the product of two partial theta functions. In this note, I discuss the relation between the Andrews-Warnaar identity and the (1986) product formula due to Gasper and Rahman. I employ nonterminating extension of Sears-Carlitz transformation for 3\phi_2 to provide a new elegant proof for a companion identity for the difference of two partial theta series. This difference formula first appeared in the work of Schilling-Warnaar (2002). Finally, I show that Schilling-Warnnar (2002) and Warnaar (2003) formulas are, in fact, equivalent.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/0712.4087
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