Ferreira González, CheloLópez García, José LuisPérez Sinusía, Ester2018-12-142020-07-1520180022-247X (Print)10.1016/j.jmaa.2018.03.041https://academica-e.unavarra.es/handle/2454/31777We 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 functions f(x), g(x) and h(x) are analytic in a Cassini disk Dr with foci at x = ±1 containing the interval [−1, 1]. Then, the end point of the interval x = −1 may be a regular singular point of the differential equation. The two-point Taylor expansion of the solution y(x) at the end points ±1 is used to study the space of analytic solutions in Dr of the differential equation, and to give a criterion for the existence and uniqueness of analytic solutions of the boundary value problem. This method is constructive and provides the two-point Taylor approximation of the analytic solutions when they exist.18 p.application/pdfeng© 2018 Elsevier Inc. The manuscript version is made available under the CC BY-NC-ND 4.0 license.Second-order linear differential equationsRegular singular pointBoundary value problemFrobenius methodTwo-point Taylor expansionsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessAcceso abierto / Sarbide irekia