Guide to the Umbral Calculus

Guide to the Umbral Calculus

A Different Mathematical Language

Silvia Licciardi, Giuseppe Dattoli


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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.


  • Preface
  • Acknowledgments
  • 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
  • Bibliography
  • Index

Readership: Undergraduates, graduates and research professionals in mathematical physics.

Key Features:

  • The book comes after more than 40 years the publication of the book by S Roman Umbral Calculus, Dover (1978)
  • Since that time many things have changed the symbolic calculus became widely used in computer codes and the theory of special functions have been implemented in platforms like "Mathematica"
  • There are therefore good chances that the book will be of interest for computer scientists, applied mathematicians and physicists


Silvia Licciardi: