Author : Jocelyn Quaintance,H W Gould
Publisher : World Scientific
Page : 276 pages
File Size : 54,9 Mb
Release : 2015-10-27
Category : Mathematics
ISBN : 9789814725293
Combinatorial Identities for Stirling Numbers by Jocelyn Quaintance,H W Gould Pdf
' This book is a unique work which provides an in-depth exploration into the mathematical expertise, philosophy, and knowledge of H W Gould. It is written in a style that is accessible to the reader with basic mathematical knowledge, and yet contains material that will be of interest to the specialist in enumerative combinatorics. This book begins with exposition on the combinatorial and algebraic techniques that Professor Gould uses for proving binomial identities. These techniques are then applied to develop formulas which relate Stirling numbers of the second kind to Stirling numbers of the first kind. Professor Gould''s techniques also provide connections between both types of Stirling numbers and Bernoulli numbers. Professor Gould believes his research success comes from his intuition on how to discover combinatorial identities. This book will appeal to a wide audience and may be used either as lecture notes for a beginning graduate level combinatorics class, or as a research supplement for the specialist in enumerative combinatorics. Contents:Basic Properties of SeriesThe Binomial TheoremIterative SeriesTwo of Professor Gould''s Favorite Algebraic TechniquesVandermonde ConvolutionThe nth Difference Operator and Euler''s Finite Difference TheoremMelzak''s FormulaGeneralized Derivative FormulasStirling Numbers of the Second Kind S(n; k)Eulerian NumbersWorpitzky NumbersStirling Numbers of the First Kind s(n; k)Explicit Formulas for s(n; n — k)Number Theoretic Definitions of Stirling NumbersBernoulli NumbersAppendix A: Newton-Gregory ExpansionsAppendix B: Generalized Bernoulli and Euler Polynomials Readership: Undergraduates, graduates and researchers interested in combinatorial and algebraic techniques. Key Features:Professor Gould is an acknowledged expert in the field of Stirling number identitiesFor the first time in print, this book collects Professor''s Gould''s vast knowledge on this subject in one accessible locationThis book contains Professor Gould''s unique approaches to discovering and proving binomial identitiesThis book contains many fully-worked detailed proofs of the identities found in H W Gould''s "Combinatorial Identities: A Standardized Set of Tables Listing 500 Binomial Coefficient Summations"Keywords:Stirling Numbers of the First Kind;Stirling Numbers of the Second Kind;Bernoulli Numbers;Generalized Bernoulli Polynomials;Worpitzky Numbers;Eulerian Numbers;Binomial Theorem;Vandermonde Convolution;Euler''s Finite Difference Theorem;Melzak''s Formula "This book is a unique work that could appeal to a wide audience: from graduate students to specialists in enumerative combinatorics, to enthusiasts of Gould''s work." CERN Courier '