Journal article
Computation of Jacobi functions of the second kind for use in nearside-farside scattering theory
Journal of computational and applied mathematics, v 82(1-2), pp 447-464
15 Sep 1997
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Abstract
The nearside-farside decomposition of a partial wave series is currently being used to understand the angular scattering of atom-diatom collision systems. In this theory, it is necessary to compute Jacobi functions of the second kind on the cut. These functions are denoted by Q(n)((alpha,beta)) (cos theta), where n, alpha, beta, may be large positive integers. The Q(n)((alpha,beta))(cos theta) can be computed from a three-term linear recurrence relation provided the initial values corresponding to n = 0 and 1, are known. We derive explicit formulas for Q(0)((alpha,beta))(cos theta), Q(1)((alpha,beta))(cos theta) in terms of elementary transcendental functions. A new generating function for Jacobi functions of nonintegral degree off the cut is obtained, a special case of which yields a generating function for Q(n)((alpha,beta))(cos theta). This is used to check the numerical results, as is a Casoratian relation. We show that the recurrence for Q(n)((alpha,beta))(cos theta) is stable in the forward direction with errors growing like O(n). We also present some numerics demonstrating the success of the method.
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Details
- Title
- Computation of Jacobi functions of the second kind for use in nearside-farside scattering theory
- Creators
- J Wimp - Drexel UniversityP McCabe - University of ManchesterJNL Connor
- Publication Details
- Journal of computational and applied mathematics, v 82(1-2), pp 447-464
- Publisher
- Elsevier
- Number of pages
- 18
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:A1997XZ14300032
- Scopus ID
- 2-s2.0-0031236155
- Other Identifier
- 991019312365604721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied