Computational Techniques for the Summation of Series

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.