López García, José LuisPagola Martínez, Pedro JesúsPalacios Herrero, Pablo2024-05-242024-05-242024López, J. L., Pagola, P. J., Palacios, P. (2024) The uniform asymptotic method "saddle point near an end point" revisited. Journal of Computational and Applied Mathematics, 443, 1-13. https://doi.org/10.1016/j.cam.2024.115764.0377-042710.1016/j.cam.2024.115764https://academica-e.unavarra.es/handle/2454/48191We continue the program initiated in [López & all, 2009–2011] to simplify asymptotic methods for integrals: in this paper we revise the uniform method ‘‘saddle point near an end point’’. We obtain a more systematic version of this uniform asymptotic method where the computation of the coefficients of the asymptotic expansion is remarkably simpler than in the classical method. On the other hand, as in the standard method, the asymptotic sequence is given in terms of parabolic cylinder functions. New asymptotic expansions of the confluent hypergeometric functions 𝑀(𝑐, 𝑥∕𝛼 + 𝑐 + 1, 𝑥) and 𝑈(𝑐, 𝛼𝑥 + 𝑐 + 1, 𝑥) for large 𝑥, 𝑐 fixed, uniformly valid for 𝛼 ∈ (0, ∞), are given as an illustration.application/pdfeng© 2024 The Authors. This is an open access article under the CC BY-NC license.Asymptotic expansionsSpecial functionsUniform expansionsinfo:eu-repo/semantics/article2024-05-24info:eu-repo/semantics/openAccess