Computational techniques for the summation of series级数求和的计算技术
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作者： Anthony Sofo著
出 版 社： 中山大学出版社
出版时间： 2003-11-1字数：版次：页数： 189印刷时间： 2003/11/01开本： 16开印次：纸张： 胶版纸I S B N ： 9780306478055包装： 精装内容简介
Computational Techniques for the Summation of Series is a text on the representation of series in closed form. The book presents a unified treatment of summation of sums and series using function theoretic methods. A technique is developed based on residue theory that is useful for the summation of series of both Hypergeometric and Non-Hypergeometric type. The theory is supported by a large number of examples. The book is both a blending of continuous and discrete mathematics and, in addition to its theoretical base; it also places many of the examples in an applicable setting. This text is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in mathematics, engineering and related fields.
作者简介：
Anthony Sofo is Associate Professor at the School of Computer Science and Mathematics at Victoria University,Australia.Dr.Sofo has Published widely and is a reviewer for many mathematical journals and an editor of the journal of inequalities in pure and Applied Mathematics.His interests are in the areas of function theoretic methods and mathematical inepualities.
目录
Preface
Acknowledgments
1. SOME METHODS FOR CLOSED FORM REPRESENTATION
1Some Methods
1.1Introduction
1.2Contour Integration
1.3Use of Integral Equations
1.4Wheelon's Results
1.5Hypergeometric Functions
2A Tree Search Sum and Some Relations
2.1Binomial Summation
2.2Riordan
2.3Method of Jonassen and Knuth
2.4Method of Gessel
2.5Method of Rousseau
2.6Hypergeometric Form
2.7Snake Oil Method
2.8Some Relations
2.9Method of Sister Celine
2.10 Method of Creative Telescoping
2.11 WZ Pairs Method
2. NON-HYPERGEOMETRIC SUMMATION
1Introduction
2 Method
3Bfirmalm's Theorem and Application
4Differentiation and Integration
5Forcing Terms
6Multiple Delays, Mixed and Neutral Equations
7Bruwier Series
8Teletraffic Example
9Neutron Behaviour Example
10 A Renewal Example
11 Ruin Problems in Compound Poisson Processes
12 A Grazing System
13 Zeros of the Transcendental Equation
14 Numerical Examples
15 Euler's Work
16 Jensen's Work
17 Ramanujan's Question
18 Cohen's Modification and Extension
19 Conolly's Problem
3. BURMANN'S THEOREM
1Introduction
2Bfirmann's Theorem and Proof
2.1Applying Biirmann's Theorem
2.2The Remainder
3Convergence Region
3.1Extension of the Series
4. BINOMIAL TYPE SUMS
1Introduction
2Problem Statement
3A Recurrence Relation
4 Relations Between Gk (m) and Fk+l (m)
5. GENERALIZATION OF THE EULER SUM
1Introduction
21-Dominant Zero
2.1The System
2.2QR,K (O) Recurrences and Closed Forms
2.3Lemma and Proof of Theorem 5.1
2.4Extension of Results
……
6. HYPERGEOMETRIC SUMMATION:FIBONACCI AND RELATED SERIES
7. SUMS AND PRODUCTS OF BINOMIAL TYPE
8. SUMS OF BINOMIAL VARIATION
References
About the Author
Index
