Computational Techniques for the Summation of Series

1. Front Matter

   Pages i-xv

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2. Some Methods for Closed Form Representation

   • Anthony Sofo

   Pages 1-29

3. Non-Hypergeometric Summation

   • Anthony Sofo

   Pages 31-62

4. Bürmann’s Theorem

   • Anthony Sofo

   Pages 63-71

5. Binomial Type Sums

   • Anthony Sofo

   Pages 73-85

6. Generalization of the Euler Sum

   • Anthony Sofo

   Pages 87-109

7. Hypergeometric Summation: Fibonacci and Related Series

   • Anthony Sofo

   Pages 111-134

8. Sums and Products of Binomial Type

   • Anthony Sofo

   Pages 135-145

9. Sums of Binomial Variation

   • Anthony Sofo

   Pages 147-175

10. Back Matter

    Pages 177-189

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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.

• Hypergeometric function
• Mathematica
• contour integration
• convergence
• differential equation
• discrete mathematics
• integral
• integral equation
• integration
• residue

From the reviews:

"This book collects in one volume the author’s considerable results in the area of the summation of series and their representation in closed form, and details the techniques by which they have been obtained. … the calculations are given in plenty of detail, and closely related work which has appeared in a variety of places is conveniently collected together. That the author passes on his extensive knowledge of the literature of results for series will also be valued by the interested scholar." (Katherine Seaton, The Australian Mathematical Society Gazette, 32:1, 2005)

"The author presents an unified treatment of summation of sums and series using function theoretic methods. … No book of this type exists which attempts to give a link, by developing a comprehensive method, between non-hypergeometric and hypergeometric summation. … This book is intended for use in the fields of applied mathematics, analysis, non-hypergeometric and hypergeometric summation, summation of series and automated techniques." (Antonio López-Carmona, Zentralblatt MATH, Vol. 1059 (10), 2005)

• School of Computer Science and Mathematics, Victoria University, Melbourne, Australia

  Anthony Sofo

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