Apery Limits of Differential Equations of Order 4 and 5
(2008) Workshop on Modular Forms and String Duality 54. p.105123 Abstract
 The concept of Apery limit for second and third order differential equations is extended to fourth and fifth order equations, mainly of CalabiYau 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
 20060603  20060608
 external identifiers

 wos:000259993700005
 language
 English
 LU publication?
 yes
 id
 515edda826d548d2b1fd1680731f008b (old id 1284973)
 date added to LUP
 20160404 11:27:08
 date last changed
 20181121 21:04:56
@inproceedings{515edda826d548d2b1fd1680731f008b, abstract = {{The concept of Apery limit for second and third order differential equations is extended to fourth and fifth order equations, mainly of CalabiYau 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 = {{105123}}, publisher = {{American Mathematical Society (AMS)}}, title = {{Apery Limits of Differential Equations of Order 4 and 5}}, volume = {{54}}, year = {{2008}}, }