Bujanda Cirauqui, BlancaLópez García, José LuisPagola Martínez, Pedro Jesús2018-12-142018-12-1420180025-5718 (Print)1088-6842 (Electronic)10.1090/mcom/3389https://academica-e.unavarra.es/handle/2454/31779We consider the confluent hypergeometric function M(a, b; z) for z ∈ C and Rb >Ra > 0, and the confluent hypergeometric function U(a, b; z) for b ∈ C, Ra > 0, and Rz > 0. We derive two convergent expansions of M(a, b; z); one of them in terms of incomplete gamma functions γ(a, z) and another one in terms of rational functions of ez and z. We also derive a convergent expansion of U(a, b; z) in terms of incomplete gamma functions γ(a, z) and Γ(a, z). The expansions of M(a, b; z) hold uniformly in either Rz ≥ 0 or Rz ≤ 0; the expansion of U(a, b; z) holds uniformly in Rz > 0. The accuracy of the approximations is illustrated by means of some numerical experiments.18 p.application/pdfeng© Copyright 2018 American Mathematical SocietyConfluent hypergeometric functionsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess