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Advances in High Energy Physics
Volume 2017 (2017), Article ID 7374256, 4 pages
Research Article

Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments

1School of Science, Beijing University of Chemical Technology, Beijing 100029, China
2New Energy and Electronics, Yancheng Teachers University, Yancheng 224002, China
3CIDETEC, Instituto Politécnico Nacional, Unidad Profesional ALM, 07700 Ciudad de México, Mexico

Correspondence should be addressed to Wei Li, Chang-Yuan Chen, and Shi-Hai Dong

Received 20 December 2016; Accepted 23 January 2017; Published 26 February 2017

Academic Editor: Saber Zarrinkamar

Copyright © 2017 Wei Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. Its generating function is applied to obtain an analytical result for a class of interesting integrals involving complicated argument, that is, , where . The present method can in principle be generalizable to the integrals involving other special functions. As an illustration we also study a typical Bessel integral with a complicated argument .