Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities
Author:   Wolfram Koepf
Publisher:   Springer London Ltd
Edition:   2nd ed. 2014
ISBN:  

9781447164630


Pages:   279
Publication Date:   25 June 2014
Format:   Paperback
Availability:   Manufactured on demand   Availability explained
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Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities


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Author:   Wolfram Koepf
Publisher:   Springer London Ltd
Imprint:   Springer London Ltd
Edition:   2nd ed. 2014
Dimensions:   Width: 15.50cm , Height: 1.60cm , Length: 23.50cm
Weight:   4.569kg
ISBN:  

9781447164630


ISBN 10:   1447164636
Pages:   279
Publication Date:   25 June 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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.- Petkovˇsek’s and Van Hoeij’s Algorithm.- Differential Equations for Sums.- Hyperexponential Antiderivatives.- Holonomic Equations for Integrals.- Rodrigues Formulas and Generating Functions.

Reviews

The book under review deals with the modern algorithmic techniques for hypergeometric summation, most of which were introduced in the 1990's. ... This well-written book should be recommended for anybody who is interested in binomial summations and special functions. It should also prove useful to researchers in mathematics and/or quantum physics working in topics which associate combinatorics of special (q-)functions ... with current quantum mechanics issues. (Christian Lavault, Mathematical Reviews, August, 2015)


“The book under review deals with the modern algorithmic techniques for hypergeometric summation, most of which were introduced in the 1990’s. … This well-written book should be recommended for anybody who is interested in binomial summations and special functions. It should also prove useful to researchers in mathematics and/or quantum physics working in topics which associate combinatorics of special (q-)functions … with current quantum mechanics issues.” (Christian Lavault, Mathematical Reviews, August, 2015)


Author Information

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.

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