Computational Techniques for the Summation of Series / by Anthony Sofo.
<STRONG>Computational Techniques for the Summation of Series</STRONG> 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...
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| Format: | eBook |
| Language: | English |
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Boston, MA :
Springer US : Imprint : Springer,
2003.
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MARC
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| 245 | 1 | 0 | |a Computational Techniques for the Summation of Series / |c by Anthony Sofo. |
| 260 | |a Boston, MA : |b Springer US : |b Imprint : |b Springer, |c 2003. | ||
| 300 | |a 1 online resource (206 pages) | ||
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| 505 | 0 | |a 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. | |
| 520 | |a <STRONG>Computational Techniques for the Summation of Series</STRONG> 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. | ||
| 650 | 0 | |a Mathematics. | |
| 650 | 0 | |a Electronic data processing. | |
| 650 | 0 | |a Functional equations. | |
| 650 | 0 | |a Functions of complex variables. | |
| 650 | 0 | |a Integral transforms. | |
| 650 | 0 | |a Sequences (Mathematics) | |
| 650 | 7 | |a Electronic data processing. |2 fast |0 (OCoLC)fst00906956. | |
| 650 | 7 | |a Functional equations. |2 fast |0 (OCoLC)fst00936067. | |
| 650 | 7 | |a Functions of complex variables. |2 fast |0 (OCoLC)fst00936116. | |
| 650 | 7 | |a Integral transforms. |2 fast |0 (OCoLC)fst00975517. | |
| 650 | 7 | |a Mathematics. |2 fast |0 (OCoLC)fst01012163. | |
| 650 | 7 | |a Sequences (Mathematics) |2 fast |0 (OCoLC)fst01112884. | |
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