Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments
| Autor: | Wei Li, Chang-Yuan Chen, Shi-Hai Dong |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Advances in High Energy Physics, Vol 2017 (2017) |
| Druh dokumentu: | article |
| ISSN: | 1687-7357 1687-7365 |
| DOI: | 10.1155/2017/7374256 |
| Popis: | 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, ∫-11Pl′m′xt-1/1+t2-2xtPk′m′(x)/(1+t2-2tx)(l′+1)/2dx, where t∈(0,1). 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 ∫0∞Jn(αx2+z2)/(x2+z2)nx2m+1dx. |
| Databáze: | Directory of Open Access Journals |
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