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arXiv · 1909.00058

Can Umbral and $q$-calculus be merged?

G. Dattoli·B. Germano·K. Górska·M. R. Martinelli
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Abstract

The $q$-calculus is reformulated in terms of the umbral calculus and of the associated operational formalism. We show that new and interesting elements emerge from such a restyling. The proposed technique is applied to a different formulations of $q$ special functions, to the derivation of integrals involving ordinary and $q$-functions and to the study of $q$-special functions and polynomials.

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G. Dattoli, B. Germano, K. Górska, M. R. Martinelli. 2019-08-29. Can Umbral and $q$-calculus be merged?. https://arxiv.org/abs/1909.00058

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