Can Umbral and $q$-calculus be merged?
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...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | 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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| DOI: | 10.48550/arxiv.1909.00058 |