### Abstract

The complete p-elliptic integrals are generalizations of the complete elliptic integrals by the generalized trigonometric function sin _{p}θ 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.

Original language | English |
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Pages (from-to) | 309-321 |

Number of pages | 13 |

Journal | Ramanujan Journal |

Volume | 46 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2018 Jun 1 |

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### Keywords

- Arithmetic–geometric mean
- Brent–Salamin’s algorithm
- Complete elliptic integrals
- Generalized trigonometric functions
- p-Laplacian

### ASJC Scopus subject areas

- Algebra and Number Theory