Large degree asymptotics of generalized Bessel polynomials |
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Authors: | José Luis Ló pez |
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Affiliation: | a Departamento de Ingenieria Matématica e Informática, Universidad Pública de Navarra, 31006-Pamplona, Spain b Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands |
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Abstract: | Asymptotic expansions are given for large values of n of the generalized Bessel polynomials . The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the origin in the z-plane. New forms of expansions in terms of elementary functions valid in sectors not containing the turning points z=±i/n are derived, and a new expansion in terms of modified Bessel functions is given. Earlier asymptotic expansions of the generalized Bessel polynomials by Wong and Zhang (1997) and Dunster (2001) are discussed. |
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Keywords: | Generalized Bessel polynomials Asymptotic expansions Bessel functions Kummer functions |
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