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arXiv · 2211.03030

Linear independence of values of the $q$-exponential and related functions

Anup B. Dixit·Veekesh Kumar·Siddhi S. Pathak
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Abstract

In this paper, we establish the linear independence of values of the $q$-analogue of the exponential function, $E_q(x)$ and its derivatives at specified algebraic arguments, when $q$ is a Pisot-Vijayraghavan number. We also deduce similar results for cognate functions, such as the Tschakaloff function and certain generalized $q$-series.

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Anup B. Dixit, Veekesh Kumar, Siddhi S. Pathak. 2022-11-06. Linear independence of values of the $q$-exponential and related functions. https://arxiv.org/abs/2211.03030

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