"DIVERGENT" RAMANUJAN-TYPE SUPERCONGRUENCES

被引：32

作者：

Guillera, Jesus ^{[1
]}

Zudilin, Wadim ^{[1
]}

机构：

[1] Univ Newcastle, Sch Math & Phys Sci, Callaghan, NSW 2308, Australia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 140卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Congruence; hypergeometric series; Ramanujan-type identities for 1/pi; creative telescoping; CONGRUENCES; FORMULAS; SERIES;

D O I：

10.1090/S0002-9939-2011-10950-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

"Divergent" Ramanujan-type series for 1/pi and 1/pi(2) provide us with new nice examples of supercongruences of the same kind as those related to the convergent cases. In this paper we manage to prove three of the supercongruences by means of the Wilf-Zeilberger algorithmic technique.

引用

页码：765 / 777

页数：13

共 19 条

[1] Borwein and Bradley's Apery-like formulae for ζ(4n+3) [J].

Almkvist, G ;

Granville, A .

EXPERIMENTAL MATHEMATICS, 1999, 8 (02) :197-203

[2]

[Anonymous], 1966, GEN HYPERGEOMETRIC F

[3]

[Anonymous], 1997, B

[4]

[Anonymous], 1997, Exp. Math.

[5]

BORWEIN JM, 1988, RAMANUJAN REVISITED, P359

[6] NEW REPRESENTATIONS FOR APERY-LIKE SEQUENCES [J].

Chan, Heng Huat ;

Zudilin, Wadim .

MATHEMATIKA, 2010, 56 (01) :107-117

[7] Domb's numbers and Ramanujan-Sato type series for 1/π [J].

Chan, HH ;

Chan, SH ;

Liu, ZG .

ADVANCES IN MATHEMATICS, 2004, 186 (02) :396-410

[8]

GUILLERA J., 2010, RAMANUJAN TYPE SERIE

[9]

GUILLERA J., 2010, EXPT MATH IN PRESS

[10] Hypergeometric identities for 10 extended Ramanujan-type series [J].

Guillera, Jesus .

RAMANUJAN JOURNAL, 2008, 15 (02) :219-234

← 1 2 →