| Title | Apery Limits of Differential Equations of Order 4 and 5 |
| Authors | Gert Almkvist, Duco van Straten, Wadim Zudilin |
| Publication | MODULAR FORMS AND STRING DUALITY |
| Year | 2008 |
| Volume | 54 |
| Pages | 105 - 123 |
| Document type | Conference paper |
| Conference name | Workshop on Modular Forms and String Duality |
| Conference Date | JUN 03-08, 2006 |
| Conference Location | Banff, CANADA |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | American Mathematical Society (AMS) |
| Abstract English | The concept of Apery 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: pi(2) Catalan's constant G, Sigma(infinity)(n=1) (n/3)/n(2); pi(3), pi(3), zeta(3), pi(3)root 3, pi(4). |
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