Browsing Artículos de revista DIMI - MIIS Aldizkari artikuluak by Author "Ferreira, Chelo"
Now showing items 1-9 of 9
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Asymptotic and convergent expansions for solutions of third-order linear differential equations with a large parameter
(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 ... -
The asymptotic expansion of the swallowtail integral in the highly oscillatory region
(Elsevier, 2018) Artículo / ArtikuluaThe 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 saddle ... -
Convergent and asymptotic methods for second-order difference equations with a large parameter
(Springer, 2018) Artículo / ArtikuluaWe 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 ... -
On a modifcation of Olver's method: a special case
(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 : xm ... -
Orthogonal basis with a conicoid first mode for shape specification of optical surfaces
(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 ... -
Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions
(Taylor & Francis, 2018) Artículo / ArtikuluaWe 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
(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
(Elsevier, 2018) Artículo / ArtikuluaWe 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 ... -
Zernike-like systems in polygons and polygonal facets
(Optical Society of America, 2015) Artículo / Artikulua
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 disk. In [Diaz et all, 2014] we introduced a new Zernike ...
