Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments
Joint Authors
Chen, Chang-Yuan
Li, Wei
Dong, Shi-Hai
Source
Advances in High Energy Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-4, 4 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-02-26
Country of Publication
Egypt
No. of Pages
4
Main Subjects
Abstract EN
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, ∫ - 1 1 P l ′ m ′ x t - 1 / 1 + t 2 - 2 x t P k ′ m ′ ( x ) / ( 1 + t 2 - 2 t x ) ( l ′ + 1 ) / 2 d x , 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 ∞ J n ( α x 2 + z 2 ) / ( x 2 + z 2 ) n x 2 m + 1 d x .
American Psychological Association (APA)
Li, Wei& Chen, Chang-Yuan& Dong, Shi-Hai. 2017. Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments. Advances in High Energy Physics،Vol. 2017, no. 2017, pp.1-4.
https://search.emarefa.net/detail/BIM-1122161
Modern Language Association (MLA)
Li, Wei…[et al.]. Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments. Advances in High Energy Physics No. 2017 (2017), pp.1-4.
https://search.emarefa.net/detail/BIM-1122161
American Medical Association (AMA)
Li, Wei& Chen, Chang-Yuan& Dong, Shi-Hai. Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments. Advances in High Energy Physics. 2017. Vol. 2017, no. 2017, pp.1-4.
https://search.emarefa.net/detail/BIM-1122161
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1122161