Now showing items 1-20 of 46

    • Analysis of singular one-dimensional linear boundary value problems using two-point Taylor expansions 

      Ferreira González, Chelo Upna; López García, José Luis Upna Orcid; Pérez Sinusía, Ester Upna Orcid (University of Szeged (Hungría), 2020)   Artículo / Artikulua  OpenAccess
      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 ...
    • Analytic formulas for the evaluation of the Pearcey integral 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna (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 ...
    • An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions 

      Bujanda Cirauqui, Blanca Upna Orcid; López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Palacios Herrero, Pablo Upna Orcid (Springer, 2022)   Artículo / Artikulua  OpenAccess
      We derive new convergent expansions of the symmetric standard elliptic integral RD(x,y,z), for x,y,z∈C∖(−∞,0], in terms of elementary functions. The expansions hold uniformly for large and small values of one of the three ...
    • Analytical ray transfer matrix for the crystalline lens 

      Navarro, Rafael; Lockett-Ruiz, Verónica; López García, José Luis Upna Orcid (OSA Publishing, 2022)   Artículo / Artikulua  OpenAccess
      We present the formulation of a paraxial ray transfer or ABCD matrix for onion-type GRIN lenses. In GRIN lenses, each iso-indicial surface (IIS) can be considered a refracting optical surface. If each IIS is a shell or ...
    • Asymptotic and convergent expansions for solutions of third-order linear differential equations with a large parameter 

      Ferreira González, Chelo Upna; López García, José Luis Upna Orcid; Pérez Sinusía, Ester Upna Orcid (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 ...
    • Asymptotic behaviour of the Urbanik semigroup 

      Berg, Christian; López García, José Luis Upna Orcid (Elsevier, 2015)   Artículo / Artikulua  OpenAccess
      We revisit the product convolution semigroup of probability densities ec(t); c > 0 on the positive half-line with moments (n!)c and determine the asymptotic behaviour of ec for large and small t > 0. This shows that (n!)c ...
    • An asymptotic expansion of the hyberbolic umbilic catastrophe integral 

      Ferreira González, Chelo Upna; López García, José Luis Upna Orcid; Pérez Sinusía, Ester Upna Orcid (Springer, 2022)   Artículo / Artikulua  OpenAccess
      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 

      Ferreira González, Chelo Upna; López García, José Luis Upna Orcid; Pérez Sinusía, Ester Upna Orcid (Elsevier, 2018)   Artículo / Artikulua  OpenAccess
      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 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Pérez Sinusía, Ester Upna Orcid (MDPI, 2023)   Artículo / Artikulua  OpenAccess
      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 

      Ferreira González, Chelo Upna; López García, José Luis Upna Orcid; Pérez Sinusía, Ester Upna Orcid (Rocky Mountain Mathematics Consortium, 2015)   Artículo / Artikulua  OpenAccess
      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 expansions of the Pearcey integral 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna (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 ...
    • A convergent and asymptotic Laplace method for integrals 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Palacios Herrero, Pablo Upna Orcid (Elsevier, 2023)   Artículo / Artikulua  OpenAccess
      Watson’s lemma and Laplace’s method provide asymptotic expansions of Laplace integrals F (z) := ∫ ∞ 0 e −zf (t) g(t)dt for large values of the parameter z. They are useful tools in the asymptotic approximation of ...
    • Convergent and asymptotic methods for second-order difference equations with a large parameter 

      Ferreira González, Chelo Upna; López García, José Luis Upna Orcid; Pérez Sinusía, Ester Upna Orcid (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 ...
    • Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials 

      López García, José Luis Upna Orcid; 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 ...
    • Convergent expansions of the Bessel functions in terms of elementary functions 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna (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 ...
    • Convergent expansions of the confluent hypergeometric functions in terms of elementary functions 

      Bujanda Cirauqui, Blanca Upna Orcid; López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna (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 Orcid; López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna (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 ...
    • A convergent version of Watson’s lemma for double integrals 

      Ferreira González, Chelo Upna; López García, José Luis Upna Orcid; Pérez Sinusía, Ester Upna Orcid (Taylor & Francis, 2022)   Artículo / Artikulua  OpenAccess
      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 ...
    • Effect of high-energy ball-milling on the magnetostructural properties of a Ni45Co5Mn35Sn15 alloy 

      López García, José Luis Upna Orcid; Sánchez-Alarcos Gómez, Vicente Upna Orcid; Recarte Callado, Vicente Upna Orcid; Rodríguez Velamazán, José Alberto; Unzueta, Iraultza; García, José Ángel; Plazaola, Fernando; La Roca, Paulo Matías Upna; Pérez de Landazábal Berganzo, José Ignacio Upna Orcid (Elsevier, 2021)   Artículo / Artikulua  OpenAccess
      The effect of high-energy ball-milling on the magnetostructural properties of a Ni45Co5Mn35Sn15 alloy in austenitic phase at room temperature has been analyzed by neutron and high-resolution X-ray diffraction. The ball ...
    • An extension of the multiple Erdélyi-Kober operator and representations of the generalized hypergeometric functions 

      Karp, D. B.; López García, José Luis Upna Orcid (De Gruyter, 2018)   Artículo / Artikulua  OpenAccess
      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 ...

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