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

Shingo Takeuchi

研究成果: Article

4 引用 (Scopus)

抄録

The complete p-elliptic integrals are generalizations of the complete elliptic integrals by the generalized trigonometric function sin pθ and its half-period πp. It is shown, only for p= 4 , that the generalized p-elliptic integrals yield a computation formula of πp in terms of the arithmetic–geometric mean. This is a πp-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
出版物ステータスPublished - 2018 6 1

ASJC Scopus subject areas

  • Algebra and Number Theory

これを引用

Complete p-elliptic integrals and a computation formula of πp for p= 4. / Takeuchi, Shingo.

：: Ramanujan Journal, 巻 46, 番号 2, 01.06.2018, p. 309-321.

研究成果: Article

Takeuchi, S 2018, 'Complete p-elliptic integrals and a computation formula of πp for p= 4', Ramanujan Journal, 巻. 46, 番号 2, pp. 309-321. https://doi.org/10.1007/s11139-018-9993-y
Takeuchi S. Complete p-elliptic integrals and a computation formula of πp for p= 4. Ramanujan Journal. 2018 6 1;46(2):309-321. https://doi.org/10.1007/s11139-018-9993-y
Takeuchi, Shingo. / Complete p-elliptic integrals and a computation formula of πp for p= 4. ：: Ramanujan Journal. 2018 ; 巻 46, 番号 2. pp. 309-321.
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