Evaluate More General Integrals Involving Universal Associated Legendre Polynomials via Taylor's Theorem

• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2017,（8）
• 页码范围: 177-180
• 页数: 4页
• 语种: 英文
• DOI: 10.1088/0253-6102/68/2/177

摘要

A few important integrals involving the product of two universal associated Legendre polynomials Pl'm'(x),Pk'n'(x) and x2a(1-x2)-p-1,xb(1 ±x)-p-1 and xc(1-x2)-p-1 (1 ±-x) are evaluated using the operator form of Taylor's theorem and an integral over a single universal associated Legendre polynomial.These integrals are more general since the quantum numbers are unequal,i.e.l'≠ k'and m'≠ n'.Their selection rules are also given.We also verify the correctness of those integral formulas numerically.