Licciardi S. Guide to the Umbral Calculus...2022

Textbook in PDF format

This book covers different aspects of umbral calculus and of its more recent developments. It discusses the technical details in depth, including its relevant applications. The book has therefore manyfold scopes to introduce a mathematical tool, not widespread known as it should be; to present a complete account of the relevant capabilities through the use of different examples of applications; to provide a formal bridge between different fields of research in pure and applied.
Introduction
Operator Theory and Umbral Calculus
Umbral Formulation of Hermite Polynomials
Special Polynomials and Umbral Operators
Bessel Functions and Umbral Calculus
Bessel Functions and Umbral Trigonometries
Number Theory and Umbral Calculus
Complements and Exercises
Conclusions