Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions |
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| Authors: | T M Dunster A Gil J Segura |
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| Institution: | 1.Department of Mathematics and Statistics,San Diego State University,San Diego,USA;2.Departamento de Matemática Aplicada y CC, de la Computación, ETSI Caminos,Universidad de Cantabria,Santander,Spain;3.Departamento de Matemáticas, Estadística y Computación,Universidad de Cantabria,Santander,Spain |
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| Abstract: | Uniform asymptotic expansions involving exponential and Airy functions are obtained for Laguerre polynomials \(L_{n}^{(\alpha )}(x)\), as well as complementary confluent hypergeometric functions. The expansions are valid for n large and α small or large, uniformly for unbounded real and complex values of x. The new expansions extend the range of computability of \(L_{n}^{(\alpha )}(x)\) compared to previous expansions, in particular with respect to higher terms and large values of α. Numerical evidence of their accuracy for real and complex values of x is provided. |
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