On the Difference of Partial Theta Functions
نویسنده
چکیده
n≥0(−1) nq (n−1)n 2 xn 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 for 3φ2 to discover a beautiful companion identity for the difference of two partial theta series.
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تاریخ انتشار 2008