By Wolfram Koepf

Modern algorithmic recommendations for summation, such a lot of that have been brought within the Nineties, are constructed the following and thoroughly applied within the desktop algebra process Maple™.

The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovšek and van Hoeij for hypergeometric summation and recurrence equations, effective multivariate summation in addition to q-analogues of the above algorithms are lined. comparable algorithms touching on differential equations are thought of. An similar conception of hyperexponential integration as a result of Almkvist and Zeilberger completes the book.

The mixture of those effects provides orthogonal polynomials and (hypergeometric and q-hypergeometric) detailed services a superb algorithmic starting place. for that reason, many examples from this very lively box are given.

The fabrics lined are appropriate for an introductory path on algorithmic summation and should entice scholars and researchers alike.

Show description

Read Online or Download Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities (Universitext) PDF

Best Combinatorics books

Bent Functions: Results and Applications to Cryptography

Bent features: effects and functions to Cryptography bargains a different survey of the items of discrete arithmetic often called Boolean bent features. As those maximal, nonlinear Boolean services and their generalizations have many theoretical and useful purposes in combinatorics, coding conception, and cryptography, the textual content offers a close survey in their major effects, providing a scientific assessment in their generalizations and functions, and contemplating open difficulties in type and systematization of bent capabilities.

A First Course in Combinatorial Mathematics (Oxford Applied Mathematics and Computing Science Series)

Now in a brand new moment variation, this quantity offers a transparent and concise therapy of an more and more vital department of arithmetic. a distinct introductory survey entire with easy-to-understand examples and pattern difficulties, this article comprises info on such simple combinatorial instruments as recurrence kin, producing capabilities, prevalence matrices, and the non-exclusion precept.

Winning Solutions (Problem Books in Mathematics)

This e-book presents the mathematical instruments and problem-solving event had to effectively compete in high-level challenge fixing competitions. every one part offers vital history details after which presents quite a few labored examples and routines to aid bridge the space among what the reader may perhaps already understand and what's required for high-level competitions.

Combinatorial Designs: A Tribute to Haim Hanani (Annals of Discrete Mathematics)

Haim Hanani pioneered the ideas for developing designs and the idea of pairwise balanced designs, top on to Wilson's life Theorem. He additionally led the way in which within the examine of resolvable designs, masking and packing difficulties, latin squares, 3-designs and different combinatorial configurations.

Extra info for Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities (Universitext)

Show sample text content

Comput. Appl. Math. forty eight, 91–111 (1993)CrossRefMATHMathSciNet Koornwinder98. Koornwinder, T. H. : Identities of nonterminating sequence through Zeilberger’s set of rules. J. Comput. Appl. Math. ninety nine, 449–461 (1998)CrossRefMATHMathSciNet MZ05. Mohammed, M. , Zeilberger, D. : Sharp higher bounds for the orders of the recurrences outputted via the Zeilberger and -Zeilberger algorithms. J. Symbolic Comput. 39, 201–207 (2005)CrossRefMATHMathSciNet PR97. Paule, P. , Riese, A. : A Mathematica -analogue of Zeilberger’s set of rules in response to an algebraically inspired method of -hypergeometric telescoping. In: Ismail, M. E. H. , et al. (eds. ) Fields Institute Communications, vol. 14, pp. 179–210. American Mathematical Society, Rhode Island (1997) PS95. Paule, P. , Schorn, M. : A Mathematica model of Zeilberger’s set of rules for proving binomial coefficient identities. J. Symbolic Comput. 20, 673–698 (1995)CrossRefMATHMathSciNet PWZ96. Petkovšek, M. , Wilf, H. , Zeilberger, D. : . AK Peters, Wellesley (1996) Rainville60. Rainville, E. D. : targeted services. The MacMillan Co. , long island (1960)MATH Stölting. Stölting, G. : Algorithmische Berechnung von Summen. degree thesis, Freie Universität Berlin (1996). Todorov92. Todorov, P. : an easy evidence of the Bieberbach conjecture. Bull. Cl. Sci. , VI. Sér. , Acad. R. Belg. three 12, 335–356 (1992). vanderPoorten78. van der Poorten, A. : an evidence that Euler ignored. Apéry’s evidence of the irrationality of . Math. Intelligencer 1, 195–203 (1978)CrossRefMathSciNet Vidunas01. Vidunas, R. : Maple package deal infhsum. http://​staff. technological know-how. uva. nl/​thk/​specfun/​infhsum. mpl Vidunas02. Vidunas, R. : A Generalization of Kummer’s id. Rocky Mountain J. Math. 32, 919–936 (2002)CrossRefMATHMathSciNet Weinstein91. Weinstein, L. : The Bieberbach conjecture. Int. Math. Res. now not. five, 61–64 (1991)CrossRef Wilf94. Wilf, H. S. : A footnote on proofs of the Bieberbach-de Branges theorem. Bull. London Math. Soc. 26, 61–63 (1994)CrossRefMATHMathSciNet WZ92. Wilf, H. S. , Zeilberger, D. : An algorithmic evidence conception for hypergeometric (ordinary and “”) multisum/integral identities. Invent. Math. 108, 575–633 (1992)CrossRefMathSciNet Wilson80. Wilson, J. A. : a few hypergeometric orthogonal polynomials. Siam J. Math. Anal. eleven, 690–701 (1980)CrossRefMATHMathSciNet XT95. Xin-Rong, M. , Tian-Ming, W. : challenge 95–1. SIAM Rev. 37, ninety eight (1995)CrossRef Zeilberger90a. Zeilberger, D. : A holonomic structures method of distinct services identities. J. Comput. Appl. Math. 32, 321–368 (1990)CrossRefMATHMathSciNet Zeilberger90b. Zeilberger, D. : a quick set of rules for proving terminating hypergeometric identities. Discrete Math. eighty, 207–211 (1990)CrossRefMATHMathSciNet Zeilberger91a. Zeilberger, D. : the tactic of inventive telescoping. J. Symbolic Comput. eleven, 195–204 (1991)CrossRefMATHMathSciNet Zeilberger91b. Zeilberger, D. : A Maple software for proving hypergeometric identities. SIGSAM Bull. 25, 1–13 (1991)CrossRef Footnotes 1The sum may also have bounds because the Dixon instance has. we'd like mostly . 2“To persuade ourselves of the validity of Apéry’s evidence we'd like basically entire the subsequent workout: exhibit that (7.

Rated 4.66 of 5 – based on 34 votes