Combinatorial identities for Stirling numbers :
Quaintance, Jocelyn,
Combinatorial identities for Stirling numbers : the unpublished notes of H.W. Gould / Jocelyn Quaintance, University of Pennsylvania, USA, H.W. Gould, West Virginia University, USA. - 1 online resource (xv, 260 pages)
Includes bibliographical references (pages 253-255) and index.
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 -- Generalizied 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, n -- k) -- Number theoretic definitions of Stirling numbers -- Bernoulli numbers.
"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."--
9789814725286 9814725285
Combinatorial analysis.
Mathematical analysis.
MATHEMATICS--Algebra--Intermediate.
Combinatorial analysis.
Mathematical analysis.
Electronic books.
Electronic books.
QA164 / .Q83 2015eb
512.7
Combinatorial identities for Stirling numbers : the unpublished notes of H.W. Gould / Jocelyn Quaintance, University of Pennsylvania, USA, H.W. Gould, West Virginia University, USA. - 1 online resource (xv, 260 pages)
Includes bibliographical references (pages 253-255) and index.
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 -- Generalizied 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, n -- k) -- Number theoretic definitions of Stirling numbers -- Bernoulli numbers.
"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."--
9789814725286 9814725285
Combinatorial analysis.
Mathematical analysis.
MATHEMATICS--Algebra--Intermediate.
Combinatorial analysis.
Mathematical analysis.
Electronic books.
Electronic books.
QA164 / .Q83 2015eb
512.7