Resummation of formal series. Solutions of second order linear complex ordinary differential equations near irregular singularities
Formulae for solutions of complex ordinary differential equations in the neighbourhood of irregular singularities contain almost every time divergent series. The \(k\)-summation theory developed in the field of analytic functional equations by J. P. Ramis provides us with a tool to perform in different ways some effective calculations and to compare their results. In the case of second order differential equations, we can compute the sum of the divergent series by Borel-Padé-type approximants with orthogonal Legendre or Chebyshev generating polynomials or direct Padé-type approximants with Laguerre generating polynomials, which are a generalization of classical factorial series. We take full advantage of the possibilities of computer algebra, especially of exact rational evaluation.
scientific article; zbMATH DE number 4148469
scientific article