The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of Gauss hypergeometric functions and extend the formalism to certain generalized forms of these functions. It is shown that suggested approach is particularly efficient for evaluating integrals involving hypergeometric functions and their combination with other special functions.

Unveiling new perspectives of hypergeometric functions using umbral techniques

Dattoli G.;
2024-01-01

Abstract

The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of Gauss hypergeometric functions and extend the formalism to certain generalized forms of these functions. It is shown that suggested approach is particularly efficient for evaluating integrals involving hypergeometric functions and their combination with other special functions.
2024
Bessel functions
Gaussian functions
Hypergeometric functions
Integral representations
Umbral methods
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12079/80927
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