4 papers
Umbral Hermite representations of canonical catastrophe integrals
Giuseppe Dattoli, Roberto Ricci
Higher-order multivariable Hermite-Kampé de Fériet polynomials provide a unified construction of umbral representations for canonical catastrophe integrals. Expanding the unfolding…
Analytic umbral transmutations and Bessel moments
Roberto Ricci, Giuseppe Dattoli
We develop an analytic umbral approach to Bessel moments, using them as a concrete testbed justifying the passage from formal indicial umbral calculus to Mellin--Barnes umbral tran…
Umbral methods, function factorisation and generalisation of the Fourier transform method
Giuseppe Dattoli, Roberto Ricci, Tommaso Severati
We propose a systematic way to construct trigonometric-like functions beyond the classical sine--cosine pair by factorising rational umbral operators. The guiding idea is simple: t…
Le Roy, Lerch and Legendre chi functions and generalised Borel-Le Roy transform
Giuseppe Dattoli, Roberto Ricci
The Le Roy function has been the focus of intensive research in recent years, owing both to its relevance in analysis and its versatility in applications involving fractional diffe…