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### Apery Limits of Differential Equations of Order 4 and 5

(2008) Workshop on Modular Forms and String Duality In MODULAR FORMS AND STRING DUALITY 54. p.105-123
Abstract
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).
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
MODULAR FORMS AND STRING DUALITY
volume
54
pages
105 - 123
publisher
American Mathematical Society (AMS)
conference name
Workshop on Modular Forms and String Duality
external identifiers
• WOS:000259993700005
language
English
LU publication?
yes
id
515edda8-26d5-48d2-b1fd-1680731f008b (old id 1284973)
date added to LUP
2009-02-10 14:13:34
date last changed
2016-04-16 09:15:30
```@misc{515edda8-26d5-48d2-b1fd-1680731f008b,
abstract     = {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).},
author       = {Almkvist, Gert and van Straten, Duco and Zudilin, Wadim},
language     = {eng},
pages        = {105--123},
publisher    = {ARRAY(0x8c46110)},
series       = {MODULAR FORMS AND STRING DUALITY},
title        = {Apery Limits of Differential Equations of Order 4 and 5},
volume       = {54},
year         = {2008},
}

```