Methods for the Summation of Series

This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author’s focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding. Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.

Foreword TestimonialPrefaceBiographySymbols 1.Classical Methods from Infinitesimal Calculus2.Symbolic Methods 3.Source Formulas for Symbolic Methods 4.Methods of Using Special Function Sequences, Number Sequences, and Riordan Arrays 5.Extension Methods Bibliography Index

Tian-Xiao He received Ph. D. degrees in at Dalian University of Technology, Dalian, and Texas A&M University, College Station, respectively. Dr. He is a Professor of Mathematics at Illinois Wesleyan University and Earl and Marian A. Beling Professor of Natural Science at Illinois Wesleyan University. Dr. He has authored or co-authored over 150 research articles and 7 volumes in mathematics and is presently an editor/chief editor for several math journals.