Author	Sofo, Anthony. author
Title	Computational Techniques for the Summation of Series [electronic resource] / by Anthony Sofo
Imprint	Boston, MA : Springer US : Imprint: Springer, 2003
Connect to	http://dx.doi.org/10.1007/978-1-4615-0057-5
Descript	XV, 189 p. online resource

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

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 Burmannโs 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 EulerโsWork -- 16 Jensenโs Work -- 17 Ramanujanโs Question -- 18 Cohenโs Modification and Extension -- 19 Conollyโs Problem -- 3. Bรผrmannโs Theorem -- 1 Introduction -- 2 Bรผrmannโs 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

1. Mathematics
2. Numerical analysis
3. Difference equations
4. Functional equations
5. Functions of complex variables
6. Integral transforms
7. Operational calculus
8. Sequences (Mathematics)
9. Mathematics
10. Sequences
11. Series
12. Summability
13. Difference and Functional Equations
14. Integral Transforms
15. Operational Calculus
16. Numeric Computing
17. Functions of a Complex Variable