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Author : H. M. Srivastava
Publisher : Ellis Horwood
ISBN 13 :
Total Pages : 580 pages
Book Rating : 4.3/5 (91 download)
Download or read book A Treatise on Generating Functions written by H. M. Srivastava and published by Ellis Horwood. This book was released on 1984 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Herbert S. Wilf
Publisher : Elsevier
ISBN 13 : 1483276635
Total Pages : 193 pages
Book Rating : 4.4/5 (832 download)
Download or read book Generatingfunctionology written by Herbert S. Wilf and published by Elsevier. This book was released on 2014-05-10 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.
Author : Elna B. McBride
Publisher : Springer Science & Business Media
ISBN 13 : 364287682X
Total Pages : 109 pages
Book Rating : 4.6/5 (428 download)
Download or read book Obtaining Generating Functions written by Elna B. McBride and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the study of methods of obtaining generating functions. It is an expository work at the level of the beginning graduate student. The first part of Chapter I gives the reader the necessary definitions and basic concepts. The fundamental method of direct summation is explained and illustrated. The second part of Chapter I deals with the methods developed by Rainville. These methods are based principally on inventive manipulation of power series. Weisner's group-theoretic method is explained in detail in Chapter II and is further illustrated in Chapter III. When this method is applicable, it yields a set of at least three generating functions. In Chapter II for the Laguerre polynomials six generating functions were found. Truesdell's method is studied in Chapter IV. For a given set of functions {fez, an the success of this method depends on the existence of certain transformations. If fez, a) can be transformed into F(z, a) such that a a-; F(z, a)=F(z, a+ 1), or if fez, a) can be transformed into G(z, a) such that a a-; G(z, a)=G(z, a-I), then from each transformed function a generating function can be obtained. Truesdell's method for obtaining the transformed functions does not require any ingenuity on the user's part. Truesdell has shown how these simple results may be exploited to generate more complicated results by means of specified, systematic, and general processes. His method of obtaining generating functions is only one of these results.
Author : Sergei K. Lando
Publisher : American Mathematical Society(RI)
ISBN 13 : 9781470418199
Total Pages : 148 pages
Book Rating : 4.4/5 (181 download)
Download or read book Lectures on Generating Functions written by Sergei K. Lando and published by American Mathematical Society(RI). This book was released on 2003 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: In combinatorics, one often considers the process of enumerating objects of a certain nature, which results in a sequence of positive integers. With each such sequence, one can associate a generating function, whose properties tell us a lot about the nature of the objects being enumerated. Nowadays, the language of generating functions is the main language of enumerative combinatorics. This book is based on the course given by the author at the College of Mathematics of the Independent University of Moscow. It starts with definitions, simple properties, and numerous examples of generating func.
Author : Rajan Chattamvelli
Publisher : Springer Nature
ISBN 13 : 3031794109
Total Pages : 99 pages
Book Rating : 4.0/5 (317 download)
Download or read book Generating Functions in Engineering and the Applied Sciences written by Rajan Chattamvelli and published by Springer Nature. This book was released on 2022-05-31 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on generating functions (GFs) and their applications. It discusses commonly encountered generating functions in engineering and applied sciences, such as ordinary generating functions (OGF), exponential generating functions (EGF), probability generating functions (PGF), etc. Some new GFs like Pochhammer generating functions for both rising and falling factorials are introduced in Chapter 2. Two novel GFs called "mean deviation generating function" (MDGF) and "survival function generating function" (SFGF), are introduced in Chapter 3. The mean deviation of a variety of discrete distributions are derived using the MDGF. The last chapter discusses a large number of applications in various disciplines including algebra, analysis of algorithms, polymer chemistry, combinatorics, graph theory, number theory, reliability, epidemiology, bio-informatics, genetics, management, economics, and statistics. Some background knowledge on GFs is often assumed for courses in analysis of algorithms, advanced data structures, digital signal processing (DSP), graph theory, etc. These are usually provided by either a course on "discrete mathematics" or "introduction to combinatorics." But, GFs are also used in automata theory, bio-informatics, differential equations, DSP, number theory, physical chemistry, reliability engineering, stochastic processes, and so on. Students of these courses may not have exposure to discrete mathematics or combinatorics. This book is written in such a way that even those who do not have prior knowledge can easily follow through the chapters, and apply the lessons learned in their respective disciplines. The purpose is to give a broad exposure to commonly used techniques of combinatorial mathematics, highlighting applications in a variety of disciplines.
Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.1/5 (394 download)
Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Author : Herbert S. Wilf
Publisher : Elsevier
ISBN 13 : 0080571514
Total Pages : 239 pages
Book Rating : 4.0/5 (85 download)
Download or read book Generating Functionology written by Herbert S. Wilf and published by Elsevier. This book was released on 2013-10-22 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica(r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter. Provides new applications on the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences Features an Appendix on using MAPLE(r) and Mathematica (r) to generate functions Includes many new exercises with complete solutions at the end of each chapter
Author : George N. Watson
Publisher :
ISBN 13 :
Total Pages : 842 pages
Book Rating : 4.:/5 (7 download)
Download or read book A Treatise on the Theory of Bessel Functions written by George N. Watson and published by . This book was released on 1922 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Elna Browning McBride
Publisher : Springer
ISBN 13 : 9780387052557
Total Pages : 100 pages
Book Rating : 4.0/5 (525 download)
Download or read book Obtaining Generating Functions written by Elna Browning McBride and published by Springer. This book was released on 1971-01-01 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Colin Maclaurin
Publisher :
ISBN 13 :
Total Pages : 482 pages
Book Rating : 4.:/5 (9 download)
Download or read book A treatise of fluxions written by Colin Maclaurin and published by . This book was released on 1742 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Giovanni Ferraro
Publisher : Springer Science & Business Media
ISBN 13 : 0387734686
Total Pages : 392 pages
Book Rating : 4.3/5 (877 download)
Download or read book The Rise and Development of the Theory of Series up to the Early 1820s written by Giovanni Ferraro and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The manuscript gives a coherent and detailed account of the theory of series in the eighteenth and early nineteenth centuries. It provides in one place an account of many results that are generally to be found - if at all - scattered throughout the historical and textbook literature. It presents the subject from the viewpoint of the mathematicians of the period, and is careful to distinguish earlier conceptions from ones that prevail today.
Author : Paul J. McCarthy
Publisher : Springer Science & Business Media
ISBN 13 : 1461386209
Total Pages : 373 pages
Book Rating : 4.4/5 (613 download)
Download or read book Introduction to Arithmetical Functions written by Paul J. McCarthy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of arithmetical functions has always been one of the more active parts of the theory of numbers. The large number of papers in the bibliography, most of which were written in the last forty years, attests to its popularity. Most textbooks on the theory of numbers contain some information on arithmetical functions, usually results which are classical. My purpose is to carry the reader beyond the point at which the textbooks abandon the subject. In each chapter there are some results which can be described as contemporary, and in some chapters this is true of almost all the material. This is an introduction to the subject, not a treatise. It should not be expected that it covers every topic in the theory of arithmetical functions. The bibliography is a list of papers related to the topics that are covered, and it is at least a good approximation to a complete list within the limits I have set for myself. In the case of some of the topics omitted from or slighted in the book, I cite expository papers on those topics.
Author : Matthias Beck
Publisher : American Mathematical Soc.
ISBN 13 : 147042200X
Total Pages : 308 pages
Book Rating : 4.4/5 (74 download)
Download or read book Combinatorial Reciprocity Theorems: An Invitation to Enumerative Geometric Combinatorics written by Matthias Beck and published by American Mathematical Soc.. This book was released on 2018-12-12 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics. Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature. Topics include concise introductions to partially ordered sets, polyhedral geometry, and rational generating functions, followed by highly original chapters on subdivisions, geometric realizations of partially ordered sets, and hyperplane arrangements.
Author : Kishore K. Das,
Publisher :
ISBN 13 : 9788184120820
Total Pages : 900 pages
Book Rating : 4.1/5 (28 download)
Download or read book A Treatise On Statistical Inference & Distributions written by Kishore K. Das, and published by . This book was released on 2008-08-01 with total page 900 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written in view the students of B.Sc. (honours in Statistics), M.Sc. in Statistics, students preparing for the National Eligibility Test (NET) in Mathematical Sciences, Indian Statistical Service (ISS), Indian Administrative Service (IAS) and other state civil services examinations and Statistics as one of the subjects. The book is divided into 15 chapters. The book is a utility text and to the readers of the book it will come as a hand book at all the different levels for which the book is intended. The book starts directly with the random variables and their properties after a brief overview of probability theory. Some of the important generating functions and their properties are also been dealt with.
Author : Theodore Strong
Publisher :
ISBN 13 :
Total Pages : 570 pages
Book Rating : 4.A/5 ( download)
Download or read book A Treatise on Elementary and Higher Algebra written by Theodore Strong and published by . This book was released on 1859 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Imre Pazsit
Publisher : Elsevier
ISBN 13 : 0080550436
Total Pages : 359 pages
Book Rating : 4.0/5 (85 download)
Download or read book Neutron Fluctuations written by Imre Pazsit and published by Elsevier. This book was released on 2007-10-05 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: The transport of neutrons in a multiplying system is an area of branching processes with a clear formalism. Neutron Fluctuations presents an account of the mathematical tools used in describing branching processes, which are then used to derive a large number of properties of the neutron distribution in multiplying systems with or without an external source. In the second part of the book, the theory is applied to the description of the neutron fluctuations in nuclear reactor cores as well as in small samples of fissile material. The question of how to extract information about the system under study is discussed. In particular the measurement of the reactivity of subcritical cores, driven with various Poisson and non-Poisson (pulsed) sources, and the identification of fissile material samples, is illustrated. The book gives pragmatic information for those planning and executing and evaluating experiments on such systems. Gives a complete treatise of the mathematics of branching particle processes, and in particular neutron fluctuations, in a self-contained manner The first monograph containing the theory and application of neutron fluctuations in low power ADS (spallation and pulsed sources) Suitable as a tutorial and handbook/reference book for scientists and graduate students One of the authors is the founder of the mathematical theory of neutron fluctuations in zero power systems
Author : Evelyn Afton Ayres
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (42 download)
Download or read book Generating Functions written by Evelyn Afton Ayres and published by . This book was released on 1961 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
