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Apery Limits of Differential Equations of Order 4 and 5

Almkvist, Gert LU ; van Straten, Duco and Zudilin, Wadim (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:
author
; and
organization
publishing date
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}},
}