A summation formula and Ramanujan type series

Zhi Guo Liu

doi:10.1016/j.jmaa.2011.12.048

A summation formula and Ramanujan type series

Zhi Guo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

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

16 Scopus citations

Abstract

Using some properties of the general rising shifted factorial and the gamma function we derive a variant form of Dougall's F45 summation for the classical hypergeometric functions. This variant form allows us to derive easily many Ramanujan type series for 1/π and Ramanujan type series for some other constants.

Original language	English
Pages (from-to)	1059-1065
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	389
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2011.12.048
State	Published - 15 May 2012

Keywords

Dougall's F45 summation
Gamma function
Hypergeometric functions
Ramanujan type series

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10.1016/j.jmaa.2011.12.048

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title = "A summation formula and Ramanujan type series",

abstract = "Using some properties of the general rising shifted factorial and the gamma function we derive a variant form of Dougall's F45 summation for the classical hypergeometric functions. This variant form allows us to derive easily many Ramanujan type series for 1/π and Ramanujan type series for some other constants.",

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N2 - Using some properties of the general rising shifted factorial and the gamma function we derive a variant form of Dougall's F45 summation for the classical hypergeometric functions. This variant form allows us to derive easily many Ramanujan type series for 1/π and Ramanujan type series for some other constants.

AB - Using some properties of the general rising shifted factorial and the gamma function we derive a variant form of Dougall's F45 summation for the classical hypergeometric functions. This variant form allows us to derive easily many Ramanujan type series for 1/π and Ramanujan type series for some other constants.

KW - Dougall's F45 summation

KW - Gamma function

KW - Hypergeometric functions

KW - Ramanujan type series

UR - https://www.scopus.com/pages/publications/84856248801

U2 - 10.1016/j.jmaa.2011.12.048

DO - 10.1016/j.jmaa.2011.12.048

M3 - 文章

AN - SCOPUS:84856248801

SN - 0022-247X

VL - 389

SP - 1059

EP - 1065

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

A summation formula and Ramanujan type series

Abstract

Keywords

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