On the Siegel conjecture for second-order homogeneous linear differential equations
The paper deals with an investigation of a class of entire analytic functions (so-called \(E\)-functions), satisfying systems of linear differential equations from \(\mathbb{C}(z)\). Siegel conjectured that any \(E\)-function can be represented as a polynomial with suitable algebraic coefficients. In the present paper, it is proved that an \(E\)-function satisfies a second-order homogeneous linear differential equation with coefficients from \(\mathbb{C}(z)\) if and only if it is of a special form, which is described explicitly.
second-order homogeneous linear differential equations
scientific article; zbMATH DE number 2121383