Universal Associated Legendre Polynomials and Some Useful Definite Integrals

作     者：陈昌远 尤源 陆法林 孙东升 董世海 

作者机构：School of Physics and ElectronicsYancheng Teachers University CIDETECInstituto Politécnico NacionalUnidad Profesional ALM 

出 版 物：《Communications in Theoretical Physics》 (理论物理(英文版))

年 卷 期：2016年第66卷第8期

页      面：158-162页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：Supported by the National Natural Science Foundation of China under Grant No.11275165 partially by 20160978-SIP-IPN,Mexico 

主　　题：universal associated-Legendre polynomials definite integral partial fraction expansion parity 

摘      要：We first introduce the universal associated Legendre polynomials, which are occurred in studying the noncentral fields such as the single ring-shaped potential and then present definite integrals I;（a, τ） =∫;x;[P;（x）];/（1±x）;dx,a= 0, 1, 2, 3, 4, 5, 6, τ = 1, 2, 3, I;（b, σ） =∫;x;[P;（x）];/（1-x;）;dx,b = 0, 2, 4, 6, 8, σ = 1, 2, 3, and I;（c, κ）=∫;x;[P;（x）];/[（1-x;）;（1 ± x）]dx,c = 0, 1, 2, 3, 4, 5, 6, 7, 8, κ = 1, 2. The superindices ± in I;（a, τ） and I;（c, κ） correspond to those of the factor（1 ± x） involved in weight functions. The formulas obtained in this work and also those for integer quantum numbers l′ and m’ are very useful and unavailable in classic handbooks.