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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.