The Concrete Tetrahedron Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates - Kauers, Manuel; Paule, Peter; SpringerLink (Online service) (Vienna : Springer Vienna : Imprint: Springer, 2011)
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.
1 Introduction -- 2 Formal Power Series -- 3 Polynomials -- 4 C-Finite Sequences -- 5 Hypergeometric Series -- 6 Algebraic Functions -- 7 Holonomic Sequences and Power Series -- Appendix -- References -- Index.
Keywords: Mathematics; Algebra; Combinatorics; Number theory; Mathematics; Combinatorics; Discrete Mathematics; Number Theory; Algebra