Now showing items 37-40 of 40

    • 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 ...
    • The use of two-point Taylor expansions in singular one-dimensional boundary value problems I 

      Ferreira, Chelo; López García, José Luis; Pérez Sinusía, Ester (Elsevier, 2018)   Artículo / Artikulua
      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; Navarro, Rafael; Pérez Sinusía, Ester (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 ...