Umbral Calculus

Techniques for Pure and Applied Mathematicians

Buch | Hardcover

279 Seiten

2024
Arcler Press (Verlag)
978-1-77469-875-4 (ISBN)

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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.

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.

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.

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

Erscheinungsdatum	05.12.2023
Sprache	englisch
Maße	152 x 229 mm
Gewicht	276 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-77469-875-7 / 1774698757
ISBN-13	978-1-77469-875-4 / 9781774698754
Zustand	Neuware