Sum to Product Identities

Shaun Cooper
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Shaun Cooper: Massey University, Institute of Natural and Mathematical Science

Chapter Chapter 0 in Ramanujan's Theta Functions, 2017, pp 1-57 from Springer

Abstract: Abstract The results in this chapter are basic tools that will be used throughout the book. They include the fundamental identities for theta functions such as Jacobi’s triple product identity, the quintuple product identity, Ramanujan’s summation formula, and the q-binomial theorem. We also encounter generalizations of the sine and cosine functions. A study of the coefficients in their power series expansions leads to a system of nonlinear differential equations, called Ramanujan’s differential equations.

Date: 2017
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DOI: 10.1007/978-3-319-56172-1_1

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