Complete p-elliptic integrals and a computation formula of πp for p= 4

Shingo Takeuchi

doi:10.1007/s11139-018-9993-y

Complete p-elliptic integrals and a computation formula of π_p for p= 4

Shingo Takeuchi

研究成果: Article

9 引用（Scopus）

抜粋

The complete p-elliptic integrals are generalizations of the complete elliptic integrals by the generalized trigonometric function sin _pθ and its half-period π_p. It is shown, only for p= 4 , that the generalized p-elliptic integrals yield a computation formula of π_p in terms of the arithmetic–geometric mean. This is a π_p-version of the celebrated formula of π, independently proved by Brent and Salamin in 1976.

元の言語	English
ページ（範囲）	309-321
ページ数	13
ジャーナル	Ramanujan Journal
巻	46
発行部数	2
DOI	https://doi.org/10.1007/s11139-018-9993-y
出版物ステータス	Published - 2018 6 1

ASJC Scopus subject areas

Algebra and Number Theory

文献にアクセス

10.1007/s11139-018-9993-y

フィンガープリント Complete p-elliptic integrals and a computation formula of π<sub>p</sub> for p= 4' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

これを引用

Takeuchi, S. (2018). Complete p-elliptic integrals and a computation formula of π_p for p= 4. Ramanujan Journal, 46(2), 309-321. https://doi.org/10.1007/s11139-018-9993-y

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