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Concrete mathematics: a foundation for computer science. 2nd ed. (English) Zbl 0836.00001

Amsterdam: Addison-Wesley Publishing Group. xiii, 657 p. (1994).
A refined and improved version of what has already become a classic. The only totally new section comes at the end of the chapter on binomial coefficients. It describes Zeilberger’s algorithm which enables computers to discover and prove binomial coefficient identities. Zeilberger’s computer specialist, Shalosh B. Ekhad, has now become a prolific author. See Zbl 0668.00003 for the review of the first edition (1989).

MSC:

00A05 Mathematics in general
68-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science
11B65 Binomial coefficients; factorials; \(q\)-identities
11Axx Elementary number theory
05A10 Factorials, binomial coefficients, combinatorial functions

Citations:

Zbl 0668.00003
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Digital Library of Mathematical Functions:

§1.2(iii) Partial Fractions ‣ §1.2 Elementary Algebra ‣ Areas ‣ Chapter 1 Algebraic and Analytic Methods
§1.2(ii) Finite Series ‣ §1.2 Elementary Algebra ‣ Areas ‣ Chapter 1 Algebraic and Analytic Methods
§1.2(i) Binomial Coefficients ‣ §1.2 Elementary Algebra ‣ Areas ‣ Chapter 1 Algebraic and Analytic Methods
§24.15(ii) Tangent Numbers ‣ §24.15 Related Sequences of Numbers ‣ Properties ‣ Chapter 24 Bernoulli and Euler Polynomials
Calculus of Finite Differences ‣ §24.17(i) Summation ‣ §24.17 Mathematical Applications ‣ Applications ‣ Chapter 24 Bernoulli and Euler Polynomials
§26.14(iii) Identities ‣ §26.14 Permutations: Order Notation ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.14(ii) Generating Functions ‣ §26.14 Permutations: Order Notation ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.14(i) Definitions ‣ §26.14 Permutations: Order Notation ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.14(iv) Special Values ‣ §26.14 Permutations: Order Notation ‣ Properties ‣ Chapter 26 Combinatorial Analysis
Alternative Notations ‣ §26.1 Special Notation ‣ Notation ‣ Chapter 26 Combinatorial Analysis
Alternative Notations ‣ §26.1 Special Notation ‣ Notation ‣ Chapter 26 Combinatorial Analysis
§26.8(iii) Special Values ‣ §26.8 Set Partitions: Stirling Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.8(iv) Recurrence Relations ‣ §26.8 Set Partitions: Stirling Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.8(v) Identities ‣ §26.8 Set Partitions: Stirling Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis
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