Listar Artículos de revista - Aldizkari artikuluak por autor UPNA "Pérez Sinusía, Ester"
Mostrando ítems 1-20 de 24
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Analysis of singular one-dimensional linear boundary value problems using two-point Taylor expansions
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 ... -
Asymptotic and convergent expansions for solutions of third-order linear differential equations with a large parameter
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
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
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
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 ... -
Asymptotic expansions for Moench's integral transform of hydrology
Theis' theory (1935), later improved by Hantush & Jacob (1955) and Moench (1971), is a technique designed to study the water level in aquifers. The key formula in this theory is a certain integral transform H[g](r,t) of ... -
Convergent and asymptotic expansions of solutions of differential equations with a large parameter: Olver cases II and III
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
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
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 ... -
Generalization of Zernike polynomials for regular portions of circles and ellipses
Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit circle. Here, we present a generalization of this Zernike ... -
New recurrence relations for several classical families of polynomials
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, ... -
New series expansions for the ℋ-function of communication theory
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 ... -
New series expansions of the 3F2 function
We can use the power series definition of 3F2(a1, a2, a3; b1, b2; z) to compute this function for z in the unit disk only. In this paper we obtain new expansions of this function that are convergent in larger domains. ... -
On a modifcation of Olver's method: a special case
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
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
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
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
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
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
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) ...