Computational Techniques for the Summation of Series Book

	Preface
	Acknowledgments
1	Some Methods for Closed Form Representation	1
1	Some Methods	1
2	A Tree Search Sum and Some Relations	14
2	Non-Hypergeometric Summation	31
1	Introduction	31
2	Method	32
3	Burmann's Theorem and Application	36
4	Differentiation and Integration	39
5	Forcing Terms	40
6	Multiple Delays, Mixed and Neutral Equations	42
7	Bruwier Series	43
8	Teletraffic Example	44
9	Neutron Behaviour Example	46
10	A Renewal Example	48
11	Ruin Problems in Compound Poisson Processes	50
12	A Grazing System	50
13	Zeros of the Transcendental Equation	51
14	Numerical Examples	53
15	Euler's Work	53
16	Jensen's Work	55
17	Ramanujan's Question	57
18	Cohen's Modifications and Extension	57
19	Conolly's Problem	60
3	Burmann's Theorem	63
1	Introduction	63
2	Burmann's Theorem and Proof	63
3	Convergence Region	69
4	Binomial Type Sums	73
1	Introduction	73
2	Problem Statement	73
3	A Recurrence Relation	74
4	Relations Between G[subscript k] (m) and F[subcript k+1] (m)	81
5	Generalization of the Euler Sum	87
1	Introduction	87
2	1-Dominant Zero	87
3	The k-Dominant Zeros Case	103
6	Hypergeometrics Summation: Fibonacci and Related Series	111
1	Introduction	111
2	The Difference-Delay System	111
3	The Infinite Sum	113
4	The Lagrange Form	114
5	Central Binomial Coefficients	116
6	Fibonacci, Related Polynomials and Products	123
7	Functional Forms	129
7	Sums and Products of Binomial Type	135
1	Introduction	135
2	Technique	136
3	Multiple Zeros	138
4	More Sums	142
5	Other Forcing Terms	144
8	Sums of Binomial Variation	147
1	Introduction	147
2	One Dominant Zero	147
3	Multiple Dominant Zeros	165
4	Zeros	169
5	Non-zero Forcing Terms	174
	References	177
	About the Author	185
	Index	187