期刊論文
| 學年 | 100 |
|---|---|
| 學期 | 1 |
| 出版（發表）日期 | 2011-11-01 |
| 作品名稱 | Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials |
| 作品名稱（其他語言） | |
| 著者 | Ho, Choon-Lin; Satoru Odake; Ryu Sasaki |
| 單位 | 淡江大學物理學系 |
| 出版者 | Kyiv: Natsional'na Akademiya Nauk Ukrainy * Instytut Matematyky |
| 著錄名稱、卷期、頁數 | Symmetry, Integrability and Geometry: Methods and Applications 7, 107(24pages) |
| 摘要 | We present various results on the properties of the four infinite sets of the exceptional Xl polynomials discovered recently by Odake and Sasaki [Phys. Lett. B 679 (2009), 414-417; Phys. Lett. B 684 (2010), 173-176]. These Xl polynomials are global solutions of second order Fuchsian differential equations with l+3 regular singularities and their confluent limits. We derive equivalent but much simpler looking forms of the Xl polynomials. The other subjects discussed in detail are: factorisation of the Fuchsian differential operators, shape invariance, the forward and backward shift operations, invariant polynomial subspaces under the Fuchsian differential operators, the Gram-Schmidt orthonormalisation procedure, three term recurrence relations and the generating functions for the Xl polynomials. |
| 關鍵字 | exceptional orthogonal polynomials; Gram-Schmidt process; Rodrigues formulas; generating functions |
| 語言 | zh_TW |
| ISSN | 1815-0659 |
| 期刊性質 | 國外 |
| 收錄於 | |
| 產學合作 | |
| 通訊作者 | |
| 審稿制度 | |
| 國別 | UKR |
| 公開徵稿 | |
| 出版型式 | 電子版 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/96066 ) |