Description
Book SynopsisSince 1850, mathematicians have successfully applied umbral calculus in many fields of mathematics and physics. The success of umbral calculus is due to the possibility of using techniques that have simplified the technicalities of calculations, which are usually wearisome when performed with conventional methods.
Umbral Calculus: Techniques for Pure and Applied Mathematics book provides the theoretical basis and many examples of umbral calculus, including operator theory, Hermite, Frobenius-Euler, and other special polynomials, Bessel functions, and at the end, results concerning number theory within umbral calculus viewpoint.
Table of Contents
- Section 1 Introduction to Umbral Calculus and Operator Theory
- Chapter 1 Q-Functions and Distributions, Operational and Umbral Methods
- Chapter 2 Dual Numbers and Operational Umbral Methods
Section 2 Hermite Polynomials in Umbral Calculus
- Chapter 3 Identities Involving 3-Variable Hermite Polynomials Arising from Umbral Method
- Chapter 4 Some New Identities of Bernoulli, Euler and Hermite Polynomials Arising From Umbral Calculus
- Chapter 5 Voigt Transform and Umbral Image
Section 3 Special Polynomials in Umbral Calculus
- Chapter 6 Apostol-Euler Polynomials Arising from Umbral Calculus
- Chapter 7 Barnes-type Peters Polynomial with Umbral Calculus Viewpoint
- Chapter 8 Representation by Degenerate Genocchi Polynomials
- Chapter 9 Sheffer Sequences of Polynomials and Their Applications
Section 4 Frobenius-Euler Polynomials in Umbral Calculus
- Chapter 10 Umbral Calculus and the Frobenius-Euler Polynomials
- Chapter 11 Some Identities of Frobenius-Euler Polynomials Arising from Umbral Calculus
Section 5 Bessel Functions in Umbral Calculus
- Chapter 12 A Determinant Expression for the Generalized Bessel Polynomials
- Chapter 13 Integrals of Special Functions and Umbral Methods
Section 6 Number Theory and Umbral Calculus
- Chapter 14 Poly-Cauchy Numbers and Polynomials of the Second Kind with Umbral Calculus Viewpoint
- Chapter 15 Extended R-Central Bell Polynopmials with Umbral Calculus Viewpoint
