Asymptotic Approximations for Radial Spheroidal Wavefunctions with Complex Size Parameter | Zendy

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Asymptotic Approximations for Radial Spheroidal Wavefunctions with Complex Size Parameter

Author(s) -

Martin P. A.

Publication year - 2018

Publication title -

studies in applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 46

eISSN - 1467-9590

pISSN - 0022-2526

DOI - 10.1111/sapm.12199

Subject(s) - bessel function , laplace transform , wave function , separation of variables , mathematics , mathematical analysis , scattering , cylindrical harmonics , approximations of π , laplace's method , physics , quantum mechanics , orthogonal polynomials , partial differential equation , classical orthogonal polynomials , gegenbauer polynomials

Radial spheroidal wavefunctions are functions of four variables, usually denoted by m , n , x , and γ, the last of which is known as the size parameter. This parameter becomes complex when the problem of scattering of a sound pulse by a spheroid is treated using a Laplace transform with respect to time together with the method of separation of variables. Several asymptotic approximations, involving modified Bessel functions, are developed and analyzed.

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