Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities (Universitext 2nd ed. 2014)
By: Wolfram Koepf (author)Paperback
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Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system Maple (TM).The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovsek and van Hoeij for hypergeometric summation and recurrence equations, efficient multivariate summation as well as q-analogues of the above algorithms are covered. Similar algorithms concerning differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book.The combination of these results gives orthogonal polynomials and (hypergeometric and q-hypergeometric) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given.The materials covered are suitable for an introductory course on algorithmic summation and will appeal to students and researchers alike.
Prof. Dr. Wolfram Koepf is Professor for Computational Mathematics at the University of Kassel. He started his research in geometric function theory, switching towards orthogonal polynomials and special functions and towards computer algebra. In the 1990s he has written several books about the use of computer algebra in math education, followed by the first edition of his monograph Hypergeometric Summation. In 2006 his German language text book Computeralgebra appeared. Between 2002 and 2010 he was the Chairman of the Fachgruppe Computeralgebra , the largest computer algebra group world-wide, in 2010 he served as the General Chair of the most important international computer algebra symposium ISSAC in Munich. Since 2010 he serves as PC chair of the conference series CASC. As a member of the executive committee of the German Mathematical Union (DMV) he is the responsible editor of the web resource Mathematik.de.
Introduction.- The Gamma Function.- Hypergeometric Identities.- Hypergeometric Database.- Holonomic Recurrence Equations.- Gosper's Algorithm.- The Wilf-Zeilberger Method.- Zeilberger's Algorithm.- Extensions of the Algorithms.- Petkov? sek's and Van Hoeij's Algorithm.- Differential Equations for Sums.- Hyperexponential Antiderivatives.- Holonomic Equations for Integrals.- Rodrigues Formulas and Generating Functions.
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- ID: 9781447164630
2nd ed. 2014
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