LINEAR INDEPENDENCE OF VALUES OF THE <i>q</i>-EXPONENTIAL AND RELATED FUNCTIONS

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Authors

Anup B. Dixit · Institute of Mathematical Sciences

Veekesh Kumar · Indian Institute of Technology Dharwad

Siddhi Pathak · Chennai Mathematical Institute

Abstract

Abstract We establish the linear independence of values of the q -analogue of the exponential function and its derivatives at specified algebraic arguments, when q is a Pisot–Vijayaraghavan number. We also deduce similar results for cognate functions, such as the Tschakaloff function and certain generalised q -series.

Topics & Keywords

Advanced Mathematical Identities Advanced Combinatorial Mathematics Mathematical functions and polynomials

UN Sustainable Development Goals

Reduced inequalities

Publication Details

Published in: Bulletin of the Australian Mathematical Society

Volume 109, Issue 3, pp. 453-463

DOI: 10.1017/s0004972723001028

Field-Weighted Citation Impact: 0.78

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