Envíos recientes

  • Convergent and asymptotic methods for second-order difference equations with a large parameter 

    Ferreira, 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 ...
  • The asymptotic expansion of the swallowtail integral in the highly oscillatory region 

    Ferreira, 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 saddle ...
  • Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions 

    Ferreira, 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, Chelo; López García, José Luis; Pérez Sinusía, Ester (Kent State UniversityJohann Radon Institute (RICAM), 2018)   Artículo / Artikulua  OpenAccess
    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 ...
  • Asymptotic and convergent expansions for solutions of third-order linear differential equations with a large parameter 

    Ferreira, Chelo; López García, José Luis; Pérez Sinusía, Ester (Shanghai Normal UniversityWilmington Scientific Publisher, 2018)   Artículo / Artikulua  OpenAccess
    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 ...
  • Convergent expansions of the confluent hypergeometric functions in terms of elementary functions 

    Bujanda Cirauqui, Blanca Upna; López García, José Luis; Pagola Martínez, Pedro Jesús (American Mathematical Society, 2018)   Artículo / Artikulua  OpenAccess
    We consider the confluent hypergeometric function M(a, b; z) for z ∈ C and Rb >Ra > 0, and the confluent hypergeometric function U(a, b; z) for b ∈ C, Ra > 0, and Rz > 0. We derive two convergent expansions of M(a, b; z); ...
  • Convergent expansions of the incomplete gamma functions in terms of elementary functions 

    Bujanda Cirauqui, Blanca Upna; López García, José Luis; Pagola Martínez, Pedro Jesús (World Scientific Publishing, 2017)   Artículo / Artikulua  OpenAccess
    We consider the incomplete gamma function γ(a,z) for Ra>0 and z∈C. We derive several convergent expansions of z−aγ(a,z) in terms of exponentials and rational functions of z that hold uniformly in z with Rz bounded from ...
  • The use of two-point Taylor expansions in singular one-dimensional boundary value problems I 

    Ferreira, 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 ...
  • A simplification of the stationary phase method: application to the Anger and Weber functions 

    López García, José Luis (Kent State UniversityJohann Radon Institute (RICAM), 2017)   Artículo / Artikulua  OpenAccess
    The main difficulty in the practical use of the stationary phase method in asymptotic expansions of integrals is originated by a change of variables. The coefficients of the asymptotic expansion are the coefficients of the ...
  • Convergent expansions of the Bessel functions in terms of elementary functions 

    López García, José Luis; Pagola Martínez, Pedro Jesús (Springer US, 2018)   Artículo / Artikulua  OpenAccess
    We consider the Bessel functions Jν (z) and Yν (z) for ν > −1/2 and z ≥ 0. We derive a convergent expansion of Jν (z) in terms of the derivatives of (sin z)/z, and a convergent expansion of Yν (z) in terms of derivatives ...
  • Analytic formulas for the evaluation of the Pearcey integral 

    López García, José Luis; Pagola Martínez, Pedro Jesús (American Mathematical Society, 2017)   Artículo / Artikulua  OpenAccess
    We can find in the literature several convergent and/or asymptotic expansions of the Pearcey integral P(x, y) in different regions of the complex variables x and y, but they do not cover the whole complex x and y planes. The ...
  • Orthogonal basis with a conicoid first mode for shape specification of optical surfaces 

    Ferreira, Chelo; López García, José Luis; Navarro, Rafael; Pérez Sinusía, Ester (Optical Society of America, 2016)   Artículo / Artikulua  OpenAccess
    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 ...
  • The Pearcey integral in the highly oscillatory region 

    López García, José Luis; Pagola Martínez, Pedro Jesús (Elsevier, 2016)   Artículo / Artikulua  OpenAccess
    We consider the Pearcey integral P(x, y) for large values of |y| and bounded values of |x|. The integrand of the Pearcey integral oscillates wildly in this region and the asymptotic saddle point analysis is complicated. ...
  • Zernike-like systems in polygons and polygonal facets 

    Ferreira, Chelo; López García, José Luis; Navarro, Rafael; Pérez Sinusía, Ester (Optical Society of America, 2015)   Artículo / Artikulua  OpenAccess
    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 ...
  • On a modifcation of Olver's method: a special case 

    Ferreira, Chelo; López García, José Luis; Pérez Sinusía, Ester (Springer US, 2016)   Artículo / Artikulua  OpenAccess
    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 ...
  • Convergent and asymptotic expansions of the Pearcey integral 

    López García, José Luis; Pagola Martínez, Pedro Jesús (Elsevier, 2015)   Artículo / Artikulua  OpenAccess
    We consider the Pearcey integral P(x; y) for large values of |x|, x, y ∈ C. We can find in the literature several convergent or asymptotic expansions in terms of elementary and special functions, with different levels of ...
  • Super-oscillatory metalens at terahertz for enhanced focusing with reduced side lobes 

    Legaria Lerga, Santiago; Pacheco-Peña, Víctor Upna; Beruete Díaz, Miguel Upna (MDPI, 2018)   Artículo / Artikulua  OpenAccess
    In this paper, we design and numerically demonstrate an ultra-thin super-oscillatory metalens with a resolution below the diffraction limit. The zones of the lens are implemented using metasurface concepts with hexagonal ...
  • Sulfate soils stabilization with magnesium-based binders 

    Seco Meneses, Andrés; Miqueleiz, Luis; Prieto Cobo, Eduardo; Marcelino Sádaba, Sara; García, Beñat; Urmeneta, Pablo (Elsevier, 2016)   Artículo / Artikulua  OpenAccess
    Sulfate soils' stabilization is a very interesting subject with technical, economic and environmental implications. The difficulty of their stabilization is due to the fact that the usual stabilizer additives are based ...
  • Estimated and real durability of unfired clay bricks: Determining factorsand representativeness of the laboratory tests 

    Seco Meneses, Andrés; Urmeneta, Pablo; Prieto Cobo, Eduardo; García, Beñat; Miqueleiz, Luis (Elsevier, 2016)   Artículo / Artikulua  OpenAccess
    This paper presents an analysis of the representativeness of the main laboratory tests and the real dura-bility of earth-based construction materials. For this study, a natural marl soil, mixed with different per-centages ...
  • Magnesium oxide as alternative binder for unfired clay bricks manufacturing 

    Espuelas Zuazu, Sandra; Omer, Joshua; Marcelino Sádaba, Sara; Echeverría, Angel María; Seco Meneses, Andrés (Elsevier, 2017)   Artículo / Artikulua
    Replacement of fired bricks by unfired ones could be an effective way to reduce the building industryenvironmental footprint: Their manufacture not only requires less energy and natural resources but alsogenerates less waste. ...

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