Listar por autor "2476"
Mostrando ítems 1-20 de 21
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Analysis of singular one-dimensional linear boundary value problems using two-point Taylor expansions
Ferreira González, Chelo
; López García, José Luis 
; Pérez Sinusía, Ester (University of Szeged (Hungría), 2020)
Artículo / Artikulua 
We consider the second-order linear differential equation (x2 − 1)y'' + f (x)y′ + g(x)y = h(x) in the interval (−1, 1) with initial conditions or boundary conditions (Dirichlet, Neumann or mixed Dirichlet–Neumann). The ... -
Aprender matemáticas con el ordenador
Bujanda Cirauqui, Blanca ; Ferreira González, Chelo (Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, 2004)
Libro / Liburua
Los futuros perfiles profesionales de nuestros actuales alumnos universitarios están cambiando vertiginosamente. Uno de los grandes cambios es el que viene dado por la incorporación del ordenador a la mayoría (casi todos) ... -
Asymptotic and convergent expansions for solutions of third-order linear differential equations with a large parameter
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Shanghai Normal UniversityWilmington Scientific Publisher, 2018)
Artículo / Artikulua
In previous papers [6–8,10], we derived convergent and asymptotic expansions of solutions of second order linear differential equations with a large parameter. In those papers we generalized and developed special cases not ... -
Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Wiley, 2023)
Artículo / Artikulua
We consider the highly oscillatory integral 𝐹(𝑤) ∶= ∫ ∞ −∞ 𝑒𝑖𝑤(𝑡𝐾+2+𝑒𝑖𝜃𝑡𝑝) 𝑔(𝑡)𝑑𝑡 for large positive values of 𝑤, −𝜋 < 𝜃 ≤ 𝜋, 𝐾 and 𝑝 positive integers with 1 ≤ 𝑝 ≤ 𝐾, and 𝑔(𝑡) an entire function. ... -
An asymptotic expansion of the hyberbolic umbilic catastrophe integral
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Springer, 2022)
Artículo / Artikulua
We obtain an asymptotic expansion of the hyperbolic umbilic catastrophe integral Ψ(H) (x,y,z) := ∫∞−∞∫∞−∞exp(i(s3+t3+zst +yt+xs))ds dt for large values of |x| and bounded values of |y| and |z|. The expansion is given ... -
The asymptotic expansion of the swallowtail integral in the highly oscillatory region
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Elsevier, 2018)
Artículo / Artikulua
The mathematical models of many short wavelength phenomena, specially wave propagation and optical diffraction, contain, as a basic ingredient, oscillatory integrals with several nearly coincident stationary phase or ... -
Convergent and asymptotic expansions of solutions of differential equations with a large parameter: Olver cases II and III
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Rocky Mountain Mathematics Consortium, 2015)
Artículo / Artikulua
This paper continues the investigation initiated in [Lopez, 2013]. We consider the asymptotic method designed by F. Olver [Olver, 1974] for linear differential equations of the second order containing a large (asymptotic) ... -
Convergent and asymptotic methods for second-order difference equations with a large parameter
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Springer, 2018)
Artículo / Artikulua
We consider the second-order linear difference equation y(n+2)−2ay(n+1)−Λ2y(n)=g(n)y(n)+f(n)y(n+1) , where Λ is a large complex parameter, a≥0 and g and f are sequences of complex numbers. Two methods are proposed to find ... -
A convergent version of Watson’s lemma for double integrals
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Taylor & Francis, 2022)
Artículo / Artikulua
A 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 ... -
New recurrence relations for several classical families of polynomials
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Taylor and Francis, 2021)
Artículo / Artikulua
In this paper, we derive new recurrence relations for the following families of polynomials: nörlund polynomials, generalized Bernoulli polynomials, generalized Euler polynomials, Bernoulli polynomials of the second kind, ... -
On a modifcation of Olver's method: a special case
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Springer US, 2016)
Artículo / Artikulua
We consider the asymptotic method designed by Olver (Asymptotics and special functions. Academic Press, New York, 1974) for linear differential equations of the second order containing a large (asymptotic) parameter : ... -
Orthogonal basis for the optical transfer function
Ferreira González, Chelo; López García, José Luis ; Navarro, Rafael; Pérez Sinusía, Ester (Optical Society of America, 2016)
Artículo / Artikulua
We propose systems of orthogonal functions qn to represent optical transfer functions (OTF) characterized by including the diffraction-limited OTF as the first basis function q0 OTF perfect. To this end, we apply a powerful ... -
Orthogonal basis with a conicoid first mode for shape specification of optical surfaces
Ferreira González, Chelo; López García, José Luis ; Navarro, Rafael; Pérez Sinusía, Ester (Optical Society of America, 2016)
Artículo / Artikulua
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and ... -
Orthogonal basis with a conicoid first mode for shape specification of optical surfaces: reply
Ferreira González, Chelo; López García, José Luis ; Navarro, Rafael; Pérez Sinusía, Ester (Optical Society of America, 2016)
Artículo / Artikulua
We present some comments to the paper 'Orthogonal basis with a conicoid first mode for shape specification of optical surfaces: comment'. -
The swallowtail integral in the highly oscillatory region II
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Kent State UniversityJohann Radon Institute (RICAM), 2020)
Artículo / Artikulua
We analyze the asymptotic behavior of the swallowtail integral R ∞ −∞ e i(t 5+xt3+yt2+zt)dt for large values of |y| and bounded values of |x| and |z|. We use the simpli ed saddle point method introduced in [López et al., ... -
The swallowtail integral in the highly oscillatory region III
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Taylor & Francis, 2021)
Artículo / Artikulua
We consider the swallowtail integral Ψ(x,y,z):=∫∞−∞ei(t5+xt3+yt2+zt)dt for large values of |z| and bounded values of |x| and |y|. The integrand of the swallowtail integral oscillates wildly in this region and the asymptotic ... -
Uniform convergent expansions of the error function in terms of elementary functions
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Springer, 2023)
Artículo / Artikulua
We 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) ... -
Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Taylor & Francis, 2018)
Artículo / Artikulua
We 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 ... -
Uniform representation of the incomplete beta function in terms of elementary functions
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Kent State UniversityJohann Radon Institute (RICAM), 2018)
Artículo / Artikulua
We 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 <b ≤ 1 we derive a convergent expansion of z−aBz(a, b) in terms of the ... -
The use of two-point Taylor expansions in singular one-dimensional boundary value problems I
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Elsevier, 2018)
Artículo / Artikulua
We consider the second-order linear differential equation (x + 1)y′′ + f(x)y′ + g(x)y = h(x) in the interval (−1, 1) with initial conditions or boundary conditions (Dirichlet, Neumann or mixed Dirichlet-Neumann). The ...
