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

17 被引用数 (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.

本文言語 English 309-321 13 Ramanujan Journal 46 2 https://doi.org/10.1007/s11139-018-9993-y Published - 2018 6月 1

• 代数と数論

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