Personal tools
You are here: Home Publications Apéry limits of differential equations of order 4 and 5

Apéry limits of differential equations of order 4 and 5

Gert Almkvist, Duco van Straten, Wadim Zudilin

Number 36
Author Duco van Straten
Project B04
Year 2007

The concept of Apéry limit for second and third order di fferential equations is extended to fourth and fifth order equations, mainly of Calabi-Yau type. For those equations obtained from Hadamard products of second and third order equations we can prove that the limits are determined in terms of the factors by a certain formula. Otherwise the limits are found by using PSLQ in Maple and are only conjectural. All identified limits are rational linear combinations of the following numbers: π2: Catalans constant G, n=1(n3)n2,ζ(3),π33,π4.

Document Actions