@article{1b8a1549fa98428d807318b39a777f94,
title = "Complete p-elliptic integrals and a computation formula of πp for p= 4",
abstract = "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.",
keywords = "Arithmetic–geometric mean, Brent–Salamin{\textquoteright}s algorithm, Complete elliptic integrals, Generalized trigonometric functions, p-Laplacian",
author = "Shingo Takeuchi",
note = "Funding Information: This work was supported by JSPS KAKENHI Grant Number 24540218. Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2018",
month = jun,
day = "1",
doi = "10.1007/s11139-018-9993-y",
language = "English",
volume = "46",
pages = "309--321",
journal = "Ramanujan Journal",
issn = "1382-4090",
publisher = "Springer Netherlands",
number = "2",
}