Now showing items 1-5 of 5

    • 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 ...
    • 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 ...
    • 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 ...
    • 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
      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 ...