Special Formal Series Solutions of Linear Ordinary Differential Equations

A. Ryabenko ()
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A. Ryabenko: Computer Center of the Russian Academy of Science

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 356-366 from Springer

Abstract: Abstract Let be given a homogeneous linear ordinary differential equation with coefficients which are polynomial over a field K. The well known Frobenius’ algorithm [7] computes the fundamental solutions system in the neighborhood of regular singularities. These solutions are from $$\mathop K\limits^ \sim $$ [[x]][ln(x)] where $$\mathop K\limits^ \sim $$ is an algebraic extension of K. We present a new method based on the Frobenius’ algorithm. This method allows to build solutions with hypergeometric coefficients of Laurent or Puiseux series.

Date: 2000
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DOI: 10.1007/978-3-662-04166-6_32

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