# Apéry limits of differential equations of order 4 and 5

Gert Almkvist, Duco van Straten, Wadim Zudilin

Number | 36 |
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Author | Duco van Straten |

Project | B04 |

Year | 2007 |

The concept of Apéry limit for second and third order differential 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.