Evaluation of more general integrals involving universal associated Legendre polynomials

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

doi:10.1063/1.4983919

Evaluation of more general integrals involving universal associated Legendre polynomials

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

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

2 Citas (Scopus)

Resumen

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 P^m' _l' (x), P^n' _k' (x) and x^2a(1 - x²)^-p-1, x^b(1 ± x²)^-p, and x^c(1 - x²)^-p(1 ± x)^-1, where l' ≠ k' and m' ≠ n'. Their selection rules are also mentioned.

Idioma original	Inglés
Número de artículo	052105
Publicación	Journal of Mathematical Physics
Volumen	58
N.º	5
DOI	https://doi.org/10.1063/1.4983919
Estado	Publicada - 1 may. 2017

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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.",

author = "Yuan You and Chen, {Chang Yuan} and Farida Tahir and Dong, {Shi Hai}",

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doi = "10.1063/1.4983919",

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T1 - Evaluation of more general integrals involving universal associated Legendre polynomials

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AU - Chen, Chang Yuan

AU - Tahir, Farida

AU - Dong, Shi Hai

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N2 - 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.

AB - 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.

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JO - Journal of Mathematical Physics

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M1 - 052105

ER -

Evaluation of more general integrals involving universal associated Legendre polynomials

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