Gauss summation and ramanujan-type series for 1/π

Zhi Guo Liu

doi:10.1142/S1793042112500169

Gauss summation and ramanujan-type series for 1/π

Zhi Guo Liu^*

^*此作品的通讯作者

数学科学学院

科研成果: 期刊稿件 › 文章 › 同行评审

21 引用（Scopus）

摘要

Using some properties of the gamma function and the well-known Gauss summation formula for the classical hypergeometric series, we prove a four-parameter series expansion formula, which can produce infinitely many Ramanujan-type series for 1/π.

源语言	英语
页（从-至）	289-297
页数	9
期刊	International Journal of Number Theory
卷	8
期	2
DOI	https://doi.org/10.1142/S1793042112500169
出版状态	已出版 - 3月 2012

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title = "Gauss summation and ramanujan-type series for 1/π",

abstract = "Using some properties of the gamma function and the well-known Gauss summation formula for the classical hypergeometric series, we prove a four-parameter series expansion formula, which can produce infinitely many Ramanujan-type series for 1/π.",

keywords = "Euler's reflection formula, Hypergeometric series, Ramanujan-type series for 1/π, the Gauss summation",

author = "Liu, \{Zhi Guo\}",

year = "2012",

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N2 - Using some properties of the gamma function and the well-known Gauss summation formula for the classical hypergeometric series, we prove a four-parameter series expansion formula, which can produce infinitely many Ramanujan-type series for 1/π.

AB - Using some properties of the gamma function and the well-known Gauss summation formula for the classical hypergeometric series, we prove a four-parameter series expansion formula, which can produce infinitely many Ramanujan-type series for 1/π.

KW - Euler's reflection formula

KW - Hypergeometric series

KW - Ramanujan-type series for 1/π

KW - the Gauss summation

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DO - 10.1142/S1793042112500169

M3 - 文章

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SN - 1793-0421

VL - 8

SP - 289

EP - 297

JO - International Journal of Number Theory

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Gauss summation and ramanujan-type series for 1/π

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