Theory and computation of spheroidal wavefunctions

Falloon, Peter E.; Abbott, Paul; Wang, Jingbo

doi:10.1088/0305-4470/36/20/309

Cited by 99 publications

(126 citation statements)

References 13 publications

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“…On the other hand, few packages have been developed for the computation of the angular spheroidal eigenvalues λ m ℓ (c) with arbitrary complex size parameter c = c r + c i i. Thompson [19], Li et al [20,21], and Falloon et al [22] are of the most recent ones.…”

Section: Introductionmentioning

confidence: 99%

The asymptotic iteration method for the angular spheroidal eigenvalues with arbitrary complex size parameter c

Barakat¹,

Abodayeh²,

Abdallah³

et al. 2006

Can. J. Phys.

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Section: Introductionmentioning

confidence: 99%

The asymptotic iteration method for the angular spheroidal eigenvalues with arbitrary complex size parameter c

Barakat¹,

Abodayeh²,

Abdallah³

et al. 2006

Can. J. Phys.

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“…This is the method employed by the Mathematica 7.0 routine SpheroidalEigenvalue. (2) Calculation of the spheroidal harmonics S mn and R mn -According to our numerical tests and comparison with the literature results, both of these functions can be accurately computed with the Mathematica 7.0 built-in routines based on the code of Falloon et al [20]. However, the calculation of the S mn functions becomes relatively slow for large and complex size parameters (C).…”

Section: B Identification Of Possible Numerical Error Sourcesmentioning

confidence: 74%

“…(1) Determination of the eigenvalues \ mn (C) of the spheroidal angular and radial harmonics-There are several methods that can be used to evalúate the eigenvalues [3]; of these the one found to be more precise, for any size parameter C, and consistent with tabulated published results [19,20,22] is the tridiagonal matrix method [21,23]. This is the method employed by the Mathematica 7.0 routine SpheroidalEigenvalue.…”

Section: B Identification Of Possible Numerical Error Sourcesmentioning

confidence: 84%

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Near-field scattering by dielectric spheroidal particles with sizes on the order of the illuminating wavelength

et al. 2010

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We present a theoretical study of electric field scattering by wavelength-sized spheroids. The incident, internal, and scattered fields are computed analytically by a spheroidal coordínate separation-of-variables solution, assuming axially incident monochromatic illumination. The main sources of possible numerical errors are identified and an additional point-matching procedure is implemented to provide a built-in test of the validity of the results. Numerical results were obtained for prolate and óblate particles with particular aspect ratios and sizes, and a refractive índex of 1.33 relative to the surrounding médium. Special attention is paid to the characteristics of the near-field in cióse proximity to the spheroids. It is shown that particles with sizes cióse to the incident wavelength can produce high field enhancements whose spatial location and extensión can be controlled by the particle geometry.

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“…Assuming no outgroup information and equilibrium, i.e., the same model as used for deriving Equation (36), but small scaled mutation rates and the other Poisson Random Field (PRF) assumptions, RoyChoudhury and Wakely [29] derive the distribution of polymorphic sites in a sample of L loci and M haploid individuals to be Poisson with mean:…”

Section: Equilibrium Of Mutations From the Boundaries And Drift; No Omentioning

confidence: 99%

Computation of the Likelihood in Biallelic Diffusion Models Using Orthogonal Polynomials

Vogl

2014

Computation

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In population genetics, parameters describing forces such as mutation, migration and drift are generally inferred from molecular data. Lately, approximate methods based on simulations and summary statistics have been widely applied for such inference, even though these methods waste information. In contrast, probabilistic methods of inference can be shown to be optimal, if their assumptions are met. In genomic regions where recombination rates are high relative to mutation rates, polymorphic nucleotide sites can be assumed to evolve independently from each other. The distribution of allele frequencies at a large number of such sites has been called "allele-frequency spectrum" or "site-frequency spectrum" (SFS). Conditional on the allelic proportions, the likelihoods of such data can be modeled as binomial. A simple model representing the evolution of allelic proportions is the biallelic mutation-drift or mutation-directional selection-drift diffusion model. With series of orthogonal polynomials, specifically Jacobi and Gegenbauer polynomials, or the related spheroidal wave function, the diffusion equations can be solved efficiently. In the neutral case, the product of the binomial likelihoods with the sum of such polynomials leads to finite series of polynomials, i.e., relatively simple equations, from which the exact likelihoods can be calculated. In this article, the use of orthogonal polynomials for inferring population genetic parameters is investigated.

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Theory and computation of spheroidal wavefunctions

Abstract: In this paper we report on a package, written in the Mathematica computer algebra system, which has been developed to compute the spheroidal wave functions of

Cited by 99 publications

References 13 publications

The asymptotic iteration method for the angular spheroidal eigenvalues with arbitrary complex size parameter c

The asymptotic iteration method for the angular spheroidal eigenvalues with arbitrary complex size parameter c

Near-field scattering by dielectric spheroidal particles with sizes on the order of the illuminating wavelength

Computation of the Likelihood in Biallelic Diffusion Models Using Orthogonal Polynomials

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