Theory and Applications of the Generating Functions

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 Generating Functions and SeriesChapter 1 Generating Function for the Figurative Numbers of Regular Polyhedron
Chapter 2 Method for Obtaining Coefficients of Powers of Bivariate Generating Functions
Chapter 3 Danny Nguyen and IGOR PAK
Chapter 4 Generating Functions for Some Hypergeometric Functions of Four Variables via Laplace Integral Representations
Chapter 5 Identities, Inequalities for Boole-type Polynomials: Approach to Generating Functions and Infinite Series
Chapter 6 On the Exponential Generating Function for Non-Backtracking Walks
Chapter 7 Discrete Approximation by a Dirichlet Series Connected to the Riemann Zeta-Function
Chapter 8 Dirichlet Series Expansions of P-Adic L-functions

Section 2 Asymptotic Methods
Chapter 9 Asymptotic Analysis of Regular Sequences
Chapter 10 Lagrange Inversion and Combinatorial Species with Uncountable Color Palette
Chapter 11 On Solving Some Functional Equations
Chapter 12 Khinchin Families and Hayman ClassSection 3 Applications to Pure Mathematics and Applied Science
Chapter 13 Generating Functions for Generalized Stirling Type Numbers, Array Type Polynomials, Eulerian Type Polynomials and their Applications
Chapter 14 Generalized Tepper's Identity and Its Application
Chapter 15 New Bell–Sheffer Polynomial Sets