Buch, Englisch, 189 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 324 g
ISBN: 978-1-4613-4904-4
Verlag: Springer US
"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." --The Australian Mathematical Society Gazette
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
Weitere Infos & Material
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.
