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AuthorSofo, Anthony. author
TitleComputational Techniques for the Summation of Series [electronic resource] / by Anthony Sofo
ImprintBoston, MA : Springer US : Imprint: Springer, 2003
Connect tohttp://dx.doi.org/10.1007/978-1-4615-0057-5
Descript XV, 189 p. online resource

SUMMARY

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


CONTENT

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 Burmannโ{128}{153}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 Eulerโ{128}{153}sWork -- 16 Jensenโ{128}{153}s Work -- 17 Ramanujanโ{128}{153}s Question -- 18 Cohenโ{128}{153}s Modification and Extension -- 19 Conollyโ{128}{153}s Problem -- 3. Bรผrmannโ{128}{153}s Theorem -- 1 Introduction -- 2 Bรผrmannโ{128}{153}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


Mathematics Numerical analysis Difference equations Functional equations Functions of complex variables Integral transforms Operational calculus Sequences (Mathematics) Mathematics Sequences Series Summability Difference and Functional Equations Integral Transforms Operational Calculus Numeric Computing Functions of a Complex Variable



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