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Computational Techniques for the Summation of Series / by Anthony Sofo.

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<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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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Sofo, Anthony
Format: eBook
Language:English
Published: Boston, MA : Springer US : Imprint : Springer, 2003.
Subjects:
Mathematics.
Electronic data processing.
Functional equations.
Functions of complex variables.
Integral transforms.
Sequences (Mathematics)
Table of Contents:
  • 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.

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