# Near/far-side angular decompositions of Legendre polynomials using the amplitude-phase method

Near/far-side angular decompositions of Legendre polynomials using the amplitude-phase method 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 $$(l+1/2)\sin \theta$$ ( l + 1 / 2 ) sin θ , where l and $$\theta$$ θ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Chemistry Springer Journals

# Near/far-side angular decompositions of Legendre polynomials using the amplitude-phase method

, Volume 55 (8) – May 5, 2017
11 pages

/lp/springer_journal/near-far-side-angular-decompositions-of-legendre-polynomials-using-the-9SWCAB9C09
Publisher
Springer International Publishing
Subject
Chemistry; Physical Chemistry; Theoretical and Computational Chemistry; Math. Applications in Chemistry
ISSN
0259-9791
eISSN
1572-8897
D.O.I.
10.1007/s10910-017-0752-x
Publisher site
See Article on Publisher Site

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