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

研究成果: Article

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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 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
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

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