Domb's numbers and Ramanujan-Sato type series for 1/π

Heng Huat Chan; Song Heng Chan; Zhiguo Liu

doi:10.1016/j.aim.2003.07.012

Domb's numbers and Ramanujan-Sato type series for 1/π

Heng Huat Chan
, Song Heng Chan
, Zhiguo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

National University of Singapore
University of Illinois Urbana–Champaign

Research output: Contribution to journal › Article › peer-review

92 Scopus citations

Abstract

In this article, we construct a general series for 1/π. We indicate that Ramanujan's 1/π-series are all special cases of this general series and we end the paper with a new class of 1/π-series. Our work is motivated by series recently discovered by Takeshi Sato.

Original language	English
Pages (from-to)	396-410
Number of pages	15
Journal	Advances in Mathematics
Volume	186
Issue number	2
DOIs	https://doi.org/10.1016/j.aim.2003.07.012
State	Published - 20 Aug 2004

Keywords

Clausen's identity
Differential equations
Domb's numbers
Hypergeometric series
Modular equations
Ramanujan-type series
Theta functions

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10.1016/j.aim.2003.07.012

Cite this

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title = "Domb's numbers and Ramanujan-Sato type series for 1/π",

abstract = "In this article, we construct a general series for 1/π. We indicate that Ramanujan's 1/π-series are all special cases of this general series and we end the paper with a new class of 1/π-series. Our work is motivated by series recently discovered by Takeshi Sato.",

keywords = "Clausen's identity, Differential equations, Domb's numbers, Hypergeometric series, Modular equations, Ramanujan-type series, Theta functions",

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AU - Chan, Heng Huat

AU - Chan, Song Heng

AU - Liu, Zhiguo

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Y1 - 2004/8/20

N2 - In this article, we construct a general series for 1/π. We indicate that Ramanujan's 1/π-series are all special cases of this general series and we end the paper with a new class of 1/π-series. Our work is motivated by series recently discovered by Takeshi Sato.

AB - In this article, we construct a general series for 1/π. We indicate that Ramanujan's 1/π-series are all special cases of this general series and we end the paper with a new class of 1/π-series. Our work is motivated by series recently discovered by Takeshi Sato.

KW - Clausen's identity

KW - Differential equations

KW - Domb's numbers

KW - Hypergeometric series

KW - Modular equations

KW - Ramanujan-type series

KW - Theta functions

UR - https://www.scopus.com/pages/publications/3042814546

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DO - 10.1016/j.aim.2003.07.012

M3 - 文章

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SN - 0001-8708

VL - 186

SP - 396

EP - 410

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 2

ER -

Domb's numbers and Ramanujan-Sato type series for 1/π

Abstract

Keywords

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