Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials
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
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
國別 UKR
出版型式 電子版

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