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＜電子ブック＞
Computational Techniques for the Summation of Series / by Anthony Sofo

版	1st ed. 2003.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	2003
大きさ	XV, 189 p : online resource
著者標目	*Sofo, Anthony author SpringerLink (Online service)
件　名	LCSH:Sequences (Mathematics) LCSH:Difference equations LCSH:Functional equations LCSH:Mathematical analysis LCSH:Numerical analysis LCSH:Functions of complex variables FREE:Sequences, Series, Summability FREE:Difference and Functional Equations FREE:Integral Transforms and Operational Calculus FREE:Numerical Analysis FREE:Functions of a Complex Variable
一般注記	1. Some Methods for closed form Representation -- 1 Some Methods -- 2 A Tree Search Sum and Some Relations -- 2. Non-Hypergeometric Summation -- 1 Introduction -- 2 Method -- 3 Burmann’s Theorem and Application -- 4 Differentiation and Integration -- 5 Forcing Terms -- 6 Multiple Delays, Mixed and Neutral Equations -- 7 Bruwier Series -- 8 Teletraffic Example -- 9 Neutron 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’sWork -- 16 Jensen’s Work -- 17 Ramanujan’s Question -- 18 Cohen’s Modification and Extension -- 19 Conolly’s Problem -- 3. Bürmann’s Theorem -- 1 Introduction -- 2 Bürmann’s Theorem and Proof -- 3 Convergence Region -- 4. Binomial type Sums -- 1 Introduction -- 2 Problem Statement -- 3 A Recurrence Relation -- 4 Relations Between Gk (m) and Fk+1 (m) -- 5. Generalization of the Euler Sum -- 1 Introduction -- 2 1-Dominant Zero -- 3 The K-Dominant Zeros Case -- 6. Hypergeometric Summation: Fibonacci and Related Series -- 1 Introduction -- 2 The Difference-Delay System -- 3 The Infinite Sum -- 4 The Lagrange Form -- 5 Central Binomial Coefficients -- 6 Fibonacci, Related Polynomials and Products -- 7 Functional Forms -- 7. Sums and Products of Binomial Type -- 1 Introduction -- 2 Technique -- 3 Multiple Zeros -- 4 More Sums -- 5 Other Forcing Terms -- 8. Sums of Binomial Variation -- 1 Introduction -- 2 One Dominant Zero -- 3 Multiple Dominant Zeros -- 4 Zeros -- 5 Non-zero Forcing Terms -- References -- About the Author 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 HTTP:URL=https://doi.org/10.1007/978-1-4615-0057-5

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