Hypergeometric Summation : An Algorithmic Approach to Summation and Special Function Identities / by Wolfram Koepf
| データ種別 | 電子書籍 |
|---|---|
| 版 | 2nd ed. 2014. |
| 出版者 | London : Springer London : Imprint: Springer |
| 出版年 | 2014 |
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| 書誌ID | OB01025340 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | 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. License restrictions may limit access Summary: 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™. 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 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 |
| 著者標目 | *Koepf, Wolfram SpringerLink (Online service) |
| 統一書名標目 | Universitext, |
| 件 名 | LCSH:Algorithms LCSH:Computer software LCSH:Functions, special LCSH:Differential Equations LCSH:Combinatorics FREE:Algorithms FREE:Mathematical Software FREE:Special Functions FREE:Ordinary Differential Equations FREE:Combinatorics |
| 分 類 | LCC:QA76.9.A43 DC23:518.1 |
| 巻冊次 | ISBN:9781447164647 RefWorks出力（各巻） print ; ISBN:9781447164654 RefWorks出力（各巻） print ; ISBN:9781447164630 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
| 所蔵情報へのリンク | Hypergeometric summation : an algorithmic approach to summation and special function identities / Wolfram Koepf |
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