Recent Submissions

  • Order barrier for low-storage DIRK methods with positive weights 

    Higueras Sanz, Inmaculada Upna; Roldán Marrodán, Teodoro Upna (Springer, 2018)   Artículo / Artikulua  OpenAccess
    In this paper we study an order barrier for low-storage diagonally implicit Runge-Kutta (DIRK) methods with positive weights. The Butcher matrix for these schemes, that can be implemented with only two memory registers in ...
  • An efficient numerical method for singularly perturbed time dependent parabolic 2D convection-diffusion systems 

    Clavero, C.; Jorge Ulecia, Juan Carlos (Elsevier, 2018)   Artículo / Artikulua
    In this paper we deal with solving efficiently 2D linear parabolic singularly perturbed systems of convection–diffusion type. We analyze only the case of a system of two equations where both of them feature the same diffusion ...
  • Educational games to enhance museum visits for schools 

    Bossavit, Benoît Upna; Pina Calafi, Alfredo; Sánchez Gil, Isabel; Urtasun, Aitziber (National Taiwan Normal University, 2018)   Artículo / Artikulua  OpenAccess
    Museums usually look for new educational tools to enhance their exhibition. The Oteiza's museum in Navarre (Spain) especially gives importance to the dissemination of Jorge Oteiza's work to children at schools. Consequently, ...
  • A note on the asymptotic expansion of the Lerch’s transcendent 

    Cai, Xing Shi; López García, José Luis (Taylor & Francis, 2018)   Artículo / Artikulua  OpenAccess
    In Ferreira and López [Asymptotic expansions of the Hurwitz–Lerch zeta function. J Math Anal Appl. 2004;298(1):210–224], the authors derived an asymptotic expansion of the Lerch's transcendent Φ(z,s,a) for large |a|, valid ...
  • An extension of the multiple Erdélyi-Kober operator and representations of the generalized hypergeometric functions 

    Karp, B.D.; López García, José Luis (De Gruyter, 2018)   Artículo / Artikulua
    In this paper we investigate the extension of the multiple Erd elyi-Kober fractional integral operator of Kiryakova to arbitrary complex values of parameters by the way of regularization. The regularization involves ...
  • Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials 

    López García, José Luis; Temme, Nico M. (Cambridge University Press, 2004)   Artículo / Artikulua  OpenAccess
    Convergent expansions are derived for three types of orthogonal polynomials: Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for large values of the degree. The expansions are given in terms of ...
  • New asymptotic expansion and error bound for Stirling formula of reciprocal Gamma function 

    Pagola Martínez, Pedro Jesús (Ele-Math, 2018)   Artículo / Artikulua  OpenAccess
    Studying the problem about if certain probability measures are determinate by its moments [4, 8, 10] is useful to know the asymptotic behavior of the probability densities for large values of argument. This requires, ...
  • Generalization of Zernike polynomials for regular portions of circles and ellipses 

    Navarro, Rafael; López García, José Luis; Díaz, José A.; Pérez Sinusía, Ester (Optical Society of America, 2014)   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 circle. Here, we present a generalization of this Zernike ...
  • 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  OpenAccess
    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 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. ...

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