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Author: Tian-Xiao He
Publisher: CRC Press
ISBN: 1000534332
Category : Mathematics
Languages : en
Pages : 458
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Book Description
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.
Author: Tian-Xiao He
Publisher: CRC Press
ISBN: 1000534332
Category : Mathematics
Languages : en
Pages : 458
Get Book Here
Book Description
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.
Author: Bettyruth Walter
Publisher: John Benjamins Publishing
ISBN: 9027283389
Category : Language Arts & Disciplines
Languages : en
Pages : 283
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Book Description
The American courtroom trial is a speech situation. Everything occurs through the spoken word. The 'summation', as speech event embedded within the trial, which is the chronological and psychological culmination of it, is one of the few opportunities for the lawyer to communicate directly with jurors. But the speech genre summation involves preliminaries as well as the event itself; and it can affect the aftermath of the trial, for the decisions of the jurors may be influenced by this discourse.This ethnographic study considers the summation from three perspectives: that of the producer, from the point of view of the ethnographer who observed and analyzed sixty-six actual summations and from that of the receivers of the speech event who must act upon it. Information was obtained from post-deliberation questionnaires completed by 223 jurors, plus 35 alternate jurors.
Author: Hans-Friedrich Pfeiffer
Publisher: BoD – Books on Demand
ISBN: 3741292575
Category : Science
Languages : en
Pages : 68
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Book Description
This book is about Einstein's Summation Notation (ESN). It explains the rules for correct use of ESN-notation, covering the Kronecker-symbol and the Levi-Civita-symbol. Examples are taken from Linear Algebra (vector - and matrix - calculation) as well as functional analysis (diferential operators gradient, curl, divergence). The book aims at students of physics who want to deal with the Special - and General Theory of Relativity by Albert Einstein, as the correct use of ESN in this area is essential.
Author: Bernard Candelpergher
Publisher: Springer
ISBN: 3319636308
Category : Mathematics
Languages : en
Pages : 211
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Book Description
The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.
Author: Lee Jun Cai
Publisher: AcesMath!
ISBN:
Category : Mathematics
Languages : en
Pages : 31
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Book Description
Do you find your school notes too lengthy and detailed to read through? We know the agony of frantically flipping through and trying to understand the content over any revision period. This book on Summation (commonly known as the chapter as Sequences and Series) seeks to offer a condensed version of what you need to know for A-Levels H2 Mathematics, alongside with worked examples and extra practice questions. Tips on certain question types are provided to aid in smoothing the working process when dealing with them.
Author: Harold T. Davis
Publisher: Courier Corporation
ISBN: 0486789683
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Valuable as text and a reference, this concise monograph covers calculus of finite differences, gamma and psi functions, other methods of summation, summation of tables, and infinite sums. 1962 edition.
Author: L.B. W. Jolley
Publisher: Courier Corporation
ISBN: 048615338X
Category : Mathematics
Languages : en
Pages : 274
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Book Description
More than 1,200 common series appear here. Collected, summed, and grouped for easy reference, they constitute an immensely useful handbook for mathematicians, physicists, computer technicians, engineers, and students.
Author: Jürgen Gerhard
Publisher: Springer Science & Business Media
ISBN: 3540240616
Category : Computers
Languages : en
Pages : 232
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Book Description
This book brings together two streams of computer algebra: symbolic summation and integration on the one hand, and fast algorithmics on the other hand. In symbolic integration and summation, not too many algorithms with analyzed run times are known, and until now the mathematically oriented world of integration and summation and the computer science world of algorithm analysis have not had much to say to each other. The progress presented in this work towards overcoming this situation is threefold: - a clear framework for algorithm analysis with the appropriate parameters is provided, - modular algorithmic techniques are introduced in this area, and - almost optimal algorithms are presented for the basic problems.
Author: Boris V. Gnedenko
Publisher: CRC Press
ISBN: 9780849328756
Category : Mathematics
Languages : en
Pages : 282
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Book Description
This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the distribution of stock prices or surplus processes. General mathematical theory of reliability growth of modified systems, including software, is presented. Special sections deal with doubling with repair, rarefaction of renewal processes, limit theorems for supercritical Galton-Watson processes, information properties of probability distributions, and asymptotic behavior of doubly stochastic Poisson processes. Random Summation: Limit Theorems and Applications will be of use to specialists and students in probability theory, mathematical statistics, and stochastic processes, as well as to financial mathematicians, actuaries, and to engineers desiring to improve probability models for solving practical problems and for finding new approaches to the construction of mathematical models.
Author: Harold Thayer Davis
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 158
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Book Description
