The Concrete Tetrahedron: Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates (Texts & Monographs in Symbolic Computation Book 1)

The book treats four mathematical concepts which play a fundamental role in many different areas of mathematics: symbolic sums, recurrence (difference) equations, generating functions, and asymptotic estimates. Their key features, in isolation or in combination, their mastery by paper and pencil or by computer programs, and their applications to problems in pure mathematics or to "real world problems" (e.g. the analysis of algorithms) are studied. The book is intended as an algorithmic supplement to the bestselling "Concrete Mathematics" by Graham, Knuth and Patashnik. Front Matter....Pages i-ix Introduction....Pages 1-16 Formal Power Series....Pages 17-41 Polynomials....Pages 43-61 C-Finite Sequences....Pages 63-86 Hypergeometric Series....Pages 87-112 Algebraic Functions....Pages 113-136 Holonomic Sequences and Power Series....Pages 137-164 Back Matter....Pages 165-203 This book examines four mathematical concepts which play a great role in many different areas of mathematics: symbolic sums, recurrence (difference) equations, generating functions, and asymptotic estimates.