Computational Techniques for the Summation of Series [Paperback]

This book collects in one volume the authors 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. --The Australian Mathematical Society Gazette

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.- 1.1 Introduction.- 1.2 Contour Integration.- 1.3 Use of Integral Equations.- 1.4 Wheelons Results.- 1.5 Hypergeometric Functions.- 2 A Tree Search Sum and Some Relations.- 2.1 Binomial Summation.- 2.2 Riordan.- 2.3 Method of Jonassen and Knuth.- 2.4 Method of Gessel.- 2.5 Method of Rousseau.- 2.6 Hypergeometric Form.- 2.7 Snake Oil Method.- 2.8 Some Relations.- 2.9 Method of Sister Celine.- 2.10 Method of Creative Telescoping.- 2.11 WZ Pairs Method.- 2. Non-Hypergeometric Summation.- 1 Introduction.- 2 Method.- 3 Burmanns Theorem and Application.- 4 Differentiation and Integration.- 5 Forcing Terms.- 6 Multiple Delays, Mixed and Neutral Equations.- 7 Bruwier Series.- 8 Teletraffic Exampll#Ý