Last edited by Doulrajas
Saturday, July 18, 2020 | History

8 edition of Hypergeometric Summation (Viewed Advanced Lectures in Mathematics Series) found in the catalog.

# Hypergeometric Summation (Viewed Advanced Lectures in Mathematics Series)

## by Wolfram Koepf

Written in English

Subjects:
• Geometry,
• Nonfiction / Education,
• Reference,
• Mathematics,
• Science/Mathematics

• The Physical Object
FormatPaperback
Number of Pages230
ID Numbers
Open LibraryOL12768748M
ISBN 103528069503
ISBN 109783528069506

Get this from a library! Hypergeometric summation: an algorithmic approach to summation and special function identities. [Wolfram Koepf] -- Modern algorithmic techniques for summation, most of which were introduced in the s, are developed here and carefully implemented in the computer algebra system Maple [trade mark]. The algorithms. Abstract. Given a summand a n, we seek the “indefinite sum” S(n) determined (within an additive constant) by [Formula: see text] or, equivalently, by [Formula: see text] An algorithm is exhibited which, given a n, finds those S(n) with the property [Formula: see text] With this algorithm, we can determine, for example, the three identities [Formula: see text] [Formula: see text] and.

Hypergeometric Summation. Hypergeometric Summation pp | Cite as. Hypergeometric Database. Authors; Authors and affiliations; Wolfram Koepf; Chapter. First Online: 11 June k Downloads; Part of the Universitext book series (UTX) Abstract. In this chapter we list some of the major hypergeometric identities. Note that most of these. Acknowledgements: This chapter is based in part on Chapter 15 of Abramowitz and Stegun by Fritz Oberhettinger. The author thanks Richard Askey and Simon Ruijsenaars for many helpful recommendations.

The second strategy is using Sigma (a summation package in Mathematica for looking for new hypergeometric identities) to reduce the summations involving harmonic numbers. The proofs of Theorem , Theorem will be given in the next section. 2. Proofs of Theorems and By providing a simple approach to basic hypergeometric series, this book provides an excellent elementary introduction to the subject. The starting point is a simple function of several variables satisfying a number of $$q$$-difference equations.

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Different concerning the following parts of the book. Multivariate hypergeometric summation was still unfeasible when the first edition was written. In the meantime ideas by Wegschaider cleared the way. These newer developments are incorporated and illustrated in Chapter 4, and the corresponding.

In this book modern algorithmic techniques for summation, most of which have been introduced within the last decade, are developed and carefully implemented in the computer algebra system : Wolfram Koepf. “The book under review deals with the modern algorithmic techniques for hypergeometric summation, most of which were introduced in the ’s.

This well-written book should be recommended for anybody who is interested in binomial summations and special : Springer-Verlag London.

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.

Closed Form Hypergeometric Series Companion Identity Previous Exercise General Hypergeometric Series These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities Wolfram Koepf (auth.) Modern algorithmic techniques for summation, most of which were introduced in the s, are developed here and carefully implemented in the computer algebra system Maple™.

The book covers Gosper's algorithm for indefinite hypergeometric summation and Zeilberger's algorithm for definite hypergeometric summation, as well as the WZ method and extensions of these algorithms. Petkovek's decision procedure for hy- pergeometric term solutions of holonomic recurrence equations completes the picture on the summation topic.

In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic generalized hypergeometric series is sometimes just called the.

The hypergeometric function is best defined as the solution of the second order ordinary differential equation (ODE): It was Kummer (; –98) who showed that the Gauss ODE, characterized by three regular singular points at, has one solution, which is.

Hypergeometric Representations. A number of the special functions introduced in this book can be expressed in terms of hypergeometric functions.

The identification can usually be made by noting that these functions are solutions of ODEs that are special cases of the hypergeometric ODE.

Abstract. In this paper we prove a Ramanujan 1 ψ 1 summation theorem for a Laurent series extension of I.G. Macdonald’s (Schur function) multiple basic hypergeometric series of matrix argument.

This result contains as special, limiting cases our Schur function extension of the q-binomial theorem and the Jacobi triple product as in the classical case, we write our new q. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities (Universitext) - Kindle edition by Wolfram Koepf.

Download it once and read it on your Kindle device, PC, phones or tablets. Per W. Karlsson, On two hypergeometric summation formulas conjectured by Gosper, Simon Stevin 60 (), no.

4, – MR (88c) Wolfram Koepf, Hypergeometric summation, 2nd ed., Universitext, Springer, London, An algorithmic approach to summation and special function identities.

MR springer, Modern algorithmic techniques for summation, most of which were introduced in the s, are developed here and carefully implemented in the computer algebra system Maple™.The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovšek and van Hoeij for hypergeometric summation and recurrence equations, efficient multivariate summation as well as q-analogues of the above.

The package HYP allows the handling of binomial and hypergeometric series. It provides tools for manipulating factorial expressions, transforming binomial sums into hypergeometric notation, summing hypergeometric series, transforming hypergeometric series, applying contiguous relations, doing formal limits of hypergeometric expressions, transforming hypergeometric Mathematica.

Read "Hypergeometric Summation An Algorithmic Approach to Summation and Special Function Identities" by Wolfram Koepf available from Rakuten Kobo. Modern algorithmic techniques for summation, most of which were introduced in the s, are developed here and carefull Brand: Springer London.

In the following we solve the second-order differential equation called the hypergeometric differential equation using Frobenius method, named after Ferdinand Georg is a method that uses the series solution for a differential equation, where we assume the solution takes the form of a series.

This is usually the method we use for complicated ordinary differential equations. The discrete Kepler problem with initial conditions and can be solved as a hypergeometric function: The energy depends on: Finite norm states exist for an attractive potential with and.

For miscellaneous summation formulas of basic hypergeometric series, the readers can consult Gasper and Rahman. This paper is organized as follows. In Section 2, we will firstly prove Theorem from a terminating summation formula in, and.

Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities Paperback – Septem by Wolfram Koepf (Author) › Visit Amazon's Wolfram Koepf Page.

Find all the books, read about the author, and more. Cited by:. "The algorithms of Gosper, Zeilberger and Petkovsek on hypergeometric summation and recurrence equations and their q-analogues are covered, and similar algorithms on differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book.".Hypergeometric summation: an algorithmic approach to summation and special function identities.

[Wolfram Koepf] -- In this book modern algorithmic techniques for summation, most of which have been introduced within the last decade, are developed and carefully implemented in.

Abstract. We employ a one-variable extension of q-rook theory to give combinatorial proofs of some basic hypergeometric summations, including the q-Pfaff–Saalschütz summation and a $${}_4\phi _3$$ summation by Jain.