Unified solution for the Legendre equation in the interval [−1, 1]—An example of solving linear singular-ordinary differential equations

Qing-Hua Zhang, Jian Ma and Yuanyuan Qu

Applied Mathematics and Computation, 2016, vol. 289, issue C, 311-323

Abstract: This study adopts the corrected Fourier series expansion method with only limited smooth degree to solve the Legendre equation with an arbitrary complex constant μ, and finds general solution for the intervals [0, 1] and [−1, 0], which includes a logarithm singular function in forms of ln(1−x) and ln(1+x), respectively, and a nonsingular function. The smooth conjunction of these two portions at x=0 constructs the unified solution for the Legendre equation in the interval [−1, 1].

Keywords: Corrected Fourier series; Singular function; Generalized solution; Classical solution; Unified solution (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630031630337X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:289:y:2016:i:c:p:311-323

DOI: 10.1016/j.amc.2016.05.028

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().