Apery Limits of Differential Equations of Order 4 and 5
(2008) Workshop on 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:
https://lup.lub.lu.se/record/1284973
- author
- Almkvist, Gert LU ; van Straten, Duco and Zudilin, Wadim
- organization
- publishing date
- 2008
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- MODULAR FORMS AND STRING DUALITY
- volume
- 54
- pages
- 105 - 123
- publisher
- American Mathematical Society (AMS)
- conference name
- Workshop on Modular Forms and String Duality
- conference dates
- 2006-06-03 - 2006-06-08
- external identifiers
-
- wos:000259993700005
- language
- English
- LU publication?
- yes
- id
- 515edda8-26d5-48d2-b1fd-1680731f008b (old id 1284973)
- date added to LUP
- 2016-04-04 11:27:08
- date last changed
- 2018-11-21 21:04:56
@inproceedings{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}}, booktitle = {{MODULAR FORMS AND STRING DUALITY}}, language = {{eng}}, pages = {{105--123}}, publisher = {{American Mathematical Society (AMS)}}, title = {{Apery Limits of Differential Equations of Order 4 and 5}}, volume = {{54}}, year = {{2008}}, }