Umbral Calculus, a Different Mathematical Language

Abstract

This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we are referring to is that of symbolic methods, largely based on a formalism of umbral type which provides a tremendous simplification of the derivation of the associated properties. The strategy we will follow is that of establishing the rules to replace higher trascendental functions in terms of elementary functions and to take advantage from such a recasting.

It is a PhD Thesis in Mathematics and Computer Sciences, 21-02-2018, University of Catania, Italy. Supervisors: Prof. Giuseppe Dattoli, Prof. Vittorio Romano. It consists of 265 pages, 53 figures. dmi.unict.it

References in corpus (5)

• On Ramanujan Master Theorem
• Abelian Chern-Simons Vortices and Holomorphic Burgers' Hierarchy
• Rotations in three, four, and five dimensions
• A note on the Voigt profile function
• The Pseudo-Hyperbolic Functions and the Matrix Representation of Eisenstein Complex Numbers

Cited by in corpus (7)

• Operational Methods in the Study of Sobolev-Jacobi Polynomials
• Time dependent propagator for an-harmonic oscillator with quartic term in potential
• Operational vs. Umbral Methods and Borel Transform
• Repeated derivatives of tanh, sech, ... and associated polynomials
• Can Umbral and $q$-calculus be merged?
• Umbral-Algebraic Methods and Asymptotic Properties of Special Polynomials
• Generating Functions for Lacunary Legendre and Legendre-like Polynomials