Now showing items 1-20 of 35

    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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; Pérez de Landazábal Berganzo, José Ignacio Upna Orcid (Elsevier, 2021)   Artículo / Artikulua
      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 ...
    • Formulas for the amplitude of the van der Pol limit cycle through the homotopy analysis method 

      López García, José Luis Upna Orcid; Abbasbandy, S.; López Ruiz, R. Upna (Hindawi / Wiley, 2009)   Artículo / Artikulua  OpenAccess
      The limit cycle of the van der Pol oscillator, x¨+ε(x2−1)x˙+x=0, is studied in the plane (x,x˙) by applying the homotopy analysis method. A recursive set of formulas that approximate the amplitude and form of this limit ...
    • Generalization of Zernike polynomials for regular portions of circles and ellipses 

      Navarro, Rafael; López García, José Luis Upna Orcid; Díaz, José A.; Pérez Sinusía, Ester Upna Orcid (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 ...
    • New analytic representations of the hypergeometric functions p+1Fp 

      López García, José Luis Upna Orcid; Palacios Herrero, Pablo; Pagola Martínez, Pedro Jesús Upna (Springer, 2021)   Artículo / Artikulua  OpenAccess
      The power series expansions of the hypergeometric functions p+1Fp (a,b1,…,bp;c1,…,cp;z) converge either inside the unit disk |z|<1 or outside this disk |z|>1. Nørlund’s expansion in powers of z/(z−1) converges in the ...
    • New series expansions of the 3F2 function 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Pérez Sinusía, Ester Upna Orcid (2015)   Artículo / Artikulua  OpenAccess
      We can use the power series definition of 3F2(a1, a2, a3; b1, b2; z) to compute this function for z in the unit disk only. In this paper we obtain new expansions of this function that are convergent in larger domains. ...
    • A note on the asymptotic expansion of the Lerch’s transcendent 

      Cai, Xing Shi; López García, José Luis Upna Orcid (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 ...
    • On a modifcation of Olver's method: a special case 

      Ferreira González, Chelo Upna; López García, José Luis Upna Orcid; Pérez Sinusía, Ester Upna Orcid (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 : ...