Theory and Applications of the Generating Functions: Pure Mathematics and Applied Science

Cover
Half Title Page
Title Page
Copyright
Declaration
About the Editor
Table of Contents
List of Contributors
List of Abbreviations
Preface
Section 1: Generating Functions And Series
	Chapter 1: Generating Function for the Figurative Numbers of Regular Polyhedron
		Abstract
		Introduction
		Materials and Methods
		Results and Discussion
		Main Text
		Conclusion
		Data Availability
		Conflicts of Interest
		References
	Chapter 2: Method for Obtaining Coefficients of Powers of Bivariate Generating Functions
		Abstract
		Introduction
		Composita of A Multivariate Generating Function
		Operations on Compositae of Bivariate Generating Functions
		Application of Compositae for Obtaining Coefficients of Bivariate Generating Functions
		Conclusions
		References
	Chapter 3: Danny Nguyen and Igor Pak
		Abstract
		Introduction
		Notations
		Polynomial Time Operations on Short Gfs
		Short Gfs and the Class P/poly
		Short Gfs and the Non-uniform Polynomial Hierarchy
		A Hierarchy of Generating Function
		Short GFS Have Long Projection
		Intersections, Unions and Minkowski Sums of Short Gfs
		Squares, Primes, and Short GFS
		Relative Complexity of Short GF
		Proof of Lemma 4.10
		Final Remarks and Open Problems
		Acknowledgements
		References
	Chapter 4: Generating Functions for Some Hypergeometric Functions of Four Variables Via Laplace Integral Representations
		Abstract
		Introduction
		Generating Relations
		Special Cases
		Conclusion
		Acknowledgments
		References
	Chapter 5: Identities, Inequalities for Boole-type Polynomials: Approach to Generating Functions and Infinite Series
		Abstract
		Introduction
		Generating Functions for Peters Type Combinatorial Numbers And Polynomials
		Inequalities for Stirling Numbers of the Second Kind and Finite Combinatorial Sums
		Acknowledgements
		References
	Chapter 6: On the Exponential Generating Function for Non-backtracking Walks
		Abstract
		Motivation
		Background
		Exponential Generating Function for Undirected Graphs
		Exponential Generating Function for Directed Graphs
		Computing the Centrality Vectors
		Block Matrix Interpretations
		Star Graph Analysis
		Numerical Tests
		Summary
		Acknowledgements
		References
	Chapter 7: Discrete Approximation ay a Dirichlet Series Connected to the Riemann Zeta-function
		Abstract
		Introduction
		Statement Of The Main Theorem
		Proof Of Theorem 2
		Distance Between (