Wallis' sequence estimated accurately using an alternating series

DOI10.1016/j.jnt.2016.08.014zbMath1351.40003OpenAlexW2530991933MaRDI QIDQ344134

Vito Lampret

Publication date: 22 November 2016

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2016.08.014

zbMATH Keywords

rate of convergenceapproximationinequalityasymptoticestimatealternating\(\pi\)Wallis

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Special sequences and polynomials (11B83) Approximation to limiting values (summation of series, etc.) (40A25) Euler-Maclaurin formula in numerical analysis (65B15)

Related Items (7)

The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series ⋮ Simple, accurate, asymptotic estimates for the ratio of two gamma functions ⋮ How is the period of a simple pendulum growing with increasing amplitude? ⋮ Efficient approximations of finite and infinite real alternating p -series ⋮ Simple derivation of the Euler-Boole type summation formula and examples of its use ⋮ Basic asymptotic estimates for powers of Wallis’ ratios ⋮ Simple accurate balanced asymptotic approximation of Wallis' ratio using Euler-Boole alternating summation

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An asymptotic approximation of Wallis' sequence
• Refinements of Gurland's formula for pi
• Sharp inequalities and asymptotic expansion associated with the Wallis sequence
• Product Approximations via Asymptotic Integration
• Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi

This page was built for publication: Wallis' sequence estimated accurately using an alternating series