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

G. Yañez-Navarro, Guo Hua Sun, Dong Sheng Sun, Chang Yuan Chen, Shi Hai Dong

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A few important integrals involving the product of two universal associated Legendre polynomials , 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.

Original languageEnglish
Pages (from-to)177-180
Number of pages4
JournalCommunications in Theoretical Physics
Volume68
Issue number2
DOIs
StatePublished - 1 Aug 2017

Keywords

  • Taylor's theorem
  • definite integrals
  • parity
  • universal associated Legendre polynomials

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