Now showing items 1-12 of 12

    • Asymptotic and convergent expansions for solutions of third-order linear differential equations with a large parameter 

      Ferreira, Chelo; López García, José Luis Upna; Pérez Sinusía, Ester Upna (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 ...
    • The asymptotic expansion of the swallowtail integral in the highly oscillatory region 

      Ferreira, Chelo; López García, José Luis Upna; Pérez Sinusía, Ester Upna (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 methods for second-order difference equations with a large parameter 

      Ferreira, Chelo; López García, José Luis Upna; Pérez Sinusía, Ester Upna (Springer, 2018)   Artículo / Artikulua  OpenAccess
      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 ...
    • Generalization of Zernike polynomials for regular portions of circles and ellipses 

      Navarro, Rafael; López García, José Luis Upna; Díaz, José A.; Pérez Sinusía, Ester Upna (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 ...
    • On a modifcation of Olver's method: a special case 

      Ferreira, Chelo; López García, José Luis Upna; Pérez Sinusía, Ester Upna (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 ...
    • Orthogonal basis for the optical transfer function 

      Ferreira González, Chelo Upna; López García, José Luis Upna; Navarro, Rafael; Pérez Sinusía, Ester Upna (Optical Society of America, 2016)   Artículo / Artikulua  OpenAccess
      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, Chelo; López García, José Luis Upna; Navarro, Rafael; Pérez Sinusía, Ester Upna (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 ...
    • Orthogonal basis with a conicoid first mode for shape specification of optical surfaces: reply 

      Ferreira González, Chelo Upna; López García, José Luis Upna; Navarro, Rafael; Pérez Sinusía, Ester Upna (Optical Society of America, 2016)   Artículo / Artikulua  OpenAccess
      We present some comments to the paper 'Orthogonal basis with a conicoid first mode for shape specification of optical surfaces: comment'.
    • Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions 

      Ferreira, Chelo; López García, José Luis Upna; Pérez Sinusía, Ester Upna (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 Upna; Pérez Sinusía, Ester Upna (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 ...
    • The use of two-point Taylor expansions in singular one-dimensional boundary value problems I 

      Ferreira, Chelo; López García, José Luis Upna; Pérez Sinusía, Ester Upna (Elsevier, 2018)   Artículo / Artikulua  OpenAccess
      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 ...
    • Zernike-like systems in polygons and polygonal facets 

      Ferreira, Chelo; López García, José Luis Upna; Navarro, Rafael; Pérez Sinusía, Ester Upna (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 ...