Duplication formulae involving Jacobi theta functions and Gosper’s 𝑞-trigonometric functions

Mező, István

doi:10.1090/S0002-9939-2013-11576-5

Duplication formulae involving Jacobi theta functions and Gosper’s $q$-trigonometric functions
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by István Mező PDF

Proc. Amer. Math. Soc. 141 (2013), 2401-2410 Request permission

Abstract:

Using the $q$-trigonometric definitions of Gosper, we devise a new $q$-exponential function. Based on this concept, we derive a number of identities involving the Jacobi theta functions. These considerations lead to the answers to Gosper’s “mysteries”.

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