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

  • Authors:

  • José L. López;Pedro J. Pagola

  • Affiliations:

  • Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, Spain;Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, Spain

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

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Abstract

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-b0, z+a+1-b