Singular points of ordinary linear differential equations

1909/01/01 by George D. Birkhoff · 5 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Differential Equations and Numerical Methods #Meromorphic and Entire Functions

paper · pdf · doi:10.1090/s0002-9947-1909-1500848-5

Abstract

in which the functions X;ff(Z) are anaZytic or have a pote at Z oo, will transform (1) into a system of equations (1) with coefficients aij(z) of the same form (2), although q is not necessarily equal to q. Any such system of equations (1) will be said to be equivatent to (1 ) at z oo. The first part of the paper deals with the determination of the simplest system of differential equations which is equivalent to (1) at Z oo. In §1 an important Lemma on AnaZytic Fqbnctions is stated and proved. The applica-

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