On the difference of partial theta functions

Details On the difference of partial theta functions On the difference of partial theta functions

2007-12-26

arxiv.org/abs/0712.4087v1

Mathematics

Number Theory

6 pages

Scientific paper

Sums of the form add((-1)^n q^(n(n-1)/2) x^n, n>=0) are called partial theta functions. In his lost noteboook, Ramanujan recorded many identities for these functions. A few years ago Warnaar found an elegant formula for a sum of two partial theta series. Subsequently, Andrews and Warnaar established a similar result for the product of two partial theta functions. In this note we discuss the relation between the Andrews--Warnaar identity and the (1986) product formula due to Gasper and Rahman. We employ nonterminating extension of Sears--Carlitz transformation to discover a beautiful companion identity for the difference of two partial theta series.

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