Evaluation of more general integrals involving universal associated Legendre polynomials

Yuan You, Chang Yuan Chen, Farida Tahir, Shi Hai Dong

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials.We present a popular integral formula which includes universal associated Legendre polynomials and we also evaluate some important integrals involving the product of two universal associated Legendre polynomials Pm' l' (x), Pn' k' (x) and x2a(1 - x2)-p-1, xb(1 ± x2)-p, and xc(1 - x2)-p(1 ± x)-1, where l' ≠ k' and m' ≠ n'. Their selection rules are also mentioned.

Original languageEnglish
Article number052105
JournalJournal of Mathematical Physics
Volume58
Issue number5
DOIs
StatePublished - 1 May 2017

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