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Near/far-side angular decompositions of Legendre polynomials using the amplitude-phase method
KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
2017 (English)In: Journal of Mathematical Chemistry, ISSN 0259-9791, E-ISSN 1572-8897, Vol. 55, no 8, 1638-1648 p.Article in journal (Refereed) Published
Abstract [en]

A decomposition of Legendre polynomials into propagating angular waves is derived with the aid of an amplitude-phase method. This decomposition is compared with the 'Nussenzveig/Fuller' so called near/far-side decomposition of Legendre polynomials. The latter decomposition requires the Legendre function of the second kind. This is not the case with the amplitude-phase decomposition. Both representations have the same asymptotic expressions for large values of , where l and are the polynomial degree and the angle respectively. Furthermore, both components of both representations satisfy the Legendre differential equation. However, we show the two representations are not identical.

Place, publisher, year, edition, pages
Springer, 2017. Vol. 55, no 8, 1638-1648 p.
Keyword [en]
Scattering, Legendre polynomials, Amplitude-phase method, Differential cross section, Chemical reaction theory
National Category
Mathematics Chemical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-212584DOI: 10.1007/s10910-017-0752-xISI: 000407134400006OAI: oai:DiVA.org:kth-212584DiVA: diva2:1135893
Note

QC 20170824

Available from: 2017-08-24 Created: 2017-08-24 Last updated: 2017-08-24Bibliographically approved

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