Person: Ferreira González, Chelo
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Ferreira González
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Chelo
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Matemática e Informática
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2476
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Publication Open Access A convergent version of Watson’s lemma for double integrals(Taylor & Francis, 2022) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaA modification of Watson’s lemma for Laplace transforms ∞ 0 f(t) e−zt dt was introduced in [Nielsen, 1906], deriving a new asymptotic expansion for large |z| with the extra property of being convergent as well. Inspired in that idea, in this paper we derive asymptotic expansions of two-dimensional Laplace transforms F(x, y) := ∞ 0 ∞ 0 f(t,s) e−xt−ys dt ds for large |x| and |y| that are also convergent. The expansions of F(x, y) are accompanied by error bounds. Asymptotic and convergent expansions of some specialfunctions are given as illustration.Publication Open Access Uniform convergent expansions of the error function in terms of elementary functions(Springer, 2023) Ferreira González, 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 PublikoaWe derive a new analytic representation of the error function erfz in the form of a convergent series whose terms are exponential and rational functions. The expansion holds uniformly in z in the double sector | arg (±z) | <π/4. The expansion is accompanied by realistic error bounds.Publication Open Access Uniform representation of the incomplete beta function in terms of elementary functions(Kent State University, 2018) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e InformáticaWe consider the incomplete beta function Bz(a, b) in the maximum domain of analyticity of its three variables: a, b, z ∈ C, −a /∈ N, z /∈ [1, ∞). For 0. The expansions are accompanied by realistic error bounds. Some numerical experiments show the accuracy of the approximations.Publication Open Access Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions(Taylor & Francis, 2018) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e InformáticaWe consider the hypergeometric function 2F1(a, b; c; z) for z ∈ C \ [1,∞). For Ra ≥ 0, we derive a convergent expansion of 2F1(a, b; c; z) in terms of the function (1 − z)−a and of rational functions of z that is uniformly valid for z in any compact in C \ [1,∞). When a ∈ N, the expansion also contains a logarithmic term of the form log(1 − z). For Ra ≤ 0, we derive a convergent expansion of (1 − z)a 2F1(a, b; c; z) in terms of the function (1 − z)−a and of rational functions of z that is uniformly valid for z in any compact in C \ [1,∞) in the exterior of the circle |z − 1| = r for arbitrary r > 0. The expansions are accompanied by realistic error bounds. Some numerical experiments show the accuracy of the approximation.