• 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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, ...
    • 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 ...
    • 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. ...
    • 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 ...