2015•Asian-European Journal of MathematicsRequires access
On Ramanujan's general theta function and a generalization of the Borweins' cubic theta functions
Chandrashekar Adiga, Nasser Abdo Saeed Bulkhali
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Abstract
The Borwein brothers have introduced and studied three cubic theta functions. Many generalizations of these functions have been studied as well. In this paper, we introduce a new generalization of these functions and establish general formulas that are connecting our functions and Ramanujan's general theta function. Many identities found in the literature follow as a special case of our identities. We further derive general formulas for certain products of theta functions.