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López García, José Luis

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https://academica-e.unavarra.es/handle/2454/49435

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López García

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José Luis

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0002-6050-9015

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2369

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2023 - 20242
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Subject: Asymptotic expansions × Subject: Special functions ×

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Now showing 1 - 2 of 2
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    PublicationOpen Access
    The uniform asymptotic method "saddle point near an end point" revisited
    (Elsevier, 2024) López García, José Luis; Pagola Martínez, Pedro Jesús; Palacios Herrero, Pablo; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertistate Publikoa
    We 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.
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    PublicationOpen Access
    New series expansions for the ℋ-function of communication theory
    (Taylor & Francis, 2023) Ferreira, Chelo; López García, José Luis; Pérez Sinusía, Ester; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
    TheH-function of communication theory plays an important role inthe error rate analysis in digital communication with the presenceof additive white Gaussian noise (AWGN) and generalized multipathfading conditions. In this paper we investigate several convergentand/or asymptotic expansions ofHp(z,b,η)for some limiting valuesof their variables and parameters: large values ofz, large values ofp, small values ofη, and values ofb→1. We provide explicit and/orrecursive algorithms for the computation of the coefficients of theexpansions. Some numerical examples illustrate the accuracy of theapproximations.