Combinatorial Identities for Stirling Numbers

The Unpublished Notes of H W Gould

Nonfiction, Science & Nature, Mathematics, Combinatorics, Algebra
Cover of the book Combinatorial Identities for Stirling Numbers by Jocelyn Quaintance, H W Gould, World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Jocelyn Quaintance, H W Gould ISBN: 9789814725293
Publisher: World Scientific Publishing Company Publication: October 27, 2015
Imprint: WSPC Language: English
Author: Jocelyn Quaintance, H W Gould
ISBN: 9789814725293
Publisher: World Scientific Publishing Company
Publication: October 27, 2015
Imprint: WSPC
Language: English

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 Series
  • The Binomial Theorem
  • Iterative Series
  • Two of Professor Gould's Favorite Algebraic Techniques
  • Vandermonde Convolution
  • The nth Difference Operator and Euler's Finite Difference Theorem
  • Melzak's Formula
  • Generalized Derivative Formulas
  • Stirling Numbers of the Second Kind S(n; k)
  • Eulerian Numbers
  • Worpitzky Numbers
  • Stirling Numbers of the First Kind s(n; k)
  • Explicit Formulas for s(n; nk)
  • Number Theoretic Definitions of Stirling Numbers
  • Bernoulli Numbers
  • Appendix A: Newton-Gregory Expansions
  • Appendix 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 identities
  • For the first time in print, this book collects Professor's Gould's vast knowledge on this subject in one accessible location
  • This book contains Professor Gould's unique approaches to discovering and proving binomial identities
  • This 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"
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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:

Readership: Undergraduates, graduates and researchers interested in combinatorial and algebraic techniques.
Key Features:

More books from World Scientific Publishing Company

Cover of the book Understanding Service Consumers by Jocelyn Quaintance, H W Gould
Cover of the book Formal Aspects of Chinese Grammar by Jocelyn Quaintance, H W Gould
Cover of the book Harry S Truman by Jocelyn Quaintance, H W Gould
Cover of the book Quantum Bio-Informatics V by Jocelyn Quaintance, H W Gould
Cover of the book Obesity Care and Bariatric Surgery by Jocelyn Quaintance, H W Gould
Cover of the book Quantum Theory of Tunneling by Jocelyn Quaintance, H W Gould
Cover of the book Bioinformatics by Jocelyn Quaintance, H W Gould
Cover of the book Practical Strategic Management by Jocelyn Quaintance, H W Gould
Cover of the book Chiral Photochemical Scissors Targeting Proteins by Jocelyn Quaintance, H W Gould
Cover of the book Chronic Hepatitis B and C by Jocelyn Quaintance, H W Gould
Cover of the book Innovative Institutions, Public Policies and Private Strategies for Agro-Enterprise Development by Jocelyn Quaintance, H W Gould
Cover of the book International Seminar on Nuclear War and Planetary Emergencies — 45th Session by Jocelyn Quaintance, H W Gould
Cover of the book Contemporary South Korean Economy: Challenges and Prospects by Jocelyn Quaintance, H W Gould
Cover of the book The World Scientific Handbook of Energy by Jocelyn Quaintance, H W Gould
Cover of the book Global Credit Review by Jocelyn Quaintance, H W Gould
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy