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The Concrete Tetrahedron [electronic resource] :Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates / by Manuel Kauers, Peter Paule.

by Kauers, Manuel [author.]; Paule, Peter [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Texts and Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University Linz, Austria: Publisher: Vienna : Springer Vienna : 2011.Description: IX, 203 p. online resource.ISBN: 9783709104453.Subject(s): Mathematics | Algebra | Combinatorics | Number theory | Mathematics | Combinatorics | Discrete Mathematics | Number Theory | AlgebraDDC classification: 511.6 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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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.

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.

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