The confluent hypergeometric functions M(a, b; z) and U(a, b; z) for large b and z

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article; Proceedings Paper

Lopez, Jose L.¹  Pagola, Pedro J.¹ 

[1] Univ Publ Navarra, Dept Ingn Matemat & Informat, Navarra, Spain

关键词: Asymptotic expansions;    Confluent hypergeometric functions;   

DOI  :  10.1016/j.cam.2009.02.072

来源: Elsevier

【 摘 要 】

We obtain new and complete asymptotic expansions of the confluent hypergeometric functions M(a, b; z) and U(a, b; z) for large b and z. The expansions are different in the three different regions: z + a + 1 - b > 0, z + a + 1 - b < 0 and z + a + 1 - b = 0. The expansions are not of Poincare type and we give explicit expressions for the terms of the expansions. In some cases, the expansions are valid for complex values of the variables too. We give numerical examples which show the accuracy of the expansions. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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