Overview

Since 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.

Full Product Details

Author:   Stefano Spezia
Publisher:   Arcler Press
Imprint:   Arcler Press
Weight:   0.276kg
ISBN:  

9781774698754

ISBN 10:   1774698757
Pages:   279
Publication Date:   31 March 2024
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Available To Order  
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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

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Author Information

Stefano Spezia was born in Erice (Italy) in 1981. He obtained a master's degree in Electronic Engineering (Telecommunications) at the University of Palermo in 2006, and in 2012, at the same university, he got a PhD degree in Applied Physics. From 2007 to 2014, he carried out research in the Physics of Complex Ecological Systems, Semiconductor Spintronics, Nonlinear Optics and Quantum Optics, publishing several works in international journals and books. Since 2014, high school teacher of Mathematics and Physics. He is also an amateur mathematician interested in integer sequences.

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