Christian Krattenthaler

Arithmetic properties of the Taylor coefficients of differentially algebraic power series

Let f = ∑ n = 0 ∞ f n x n ∈ ℚ ¯ 〚 x 〛 be a solution of an algebraic differential equation Q ( x , y ( x ) , ⋯ , y ( k ) ( x ) ) = 0 , where Q is a multivariate polynomial with coefficients in ℚ ¯ . The sequence ( f n ) n ≥ 0 satisfies a non-linear recurrence, whose expression i...