Three essays on Machin's type formulas

DOI10.1016/j.indag.2023.07.002arXiv2302.00154OpenAlexW4385076198MaRDI QIDQ6057055

Juan Luis Varona, Armengol Gasull, Florian Luca

Publication date: 25 October 2023

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.00154

zbMATH Keywords

golden sectioncomputation of \(\pi\)Lehmer measureMachin's-type formulas

Mathematics Subject Classification ID

Numerical analysis (65-XX) Computer science (68-XX)

Cites Work

• A transform involving Chebyshev polynomials and its inversion formula
• John Machin and Robert Simson on inverse-tangent series for \(\pi\)
• On the equation \(x^2 + 2^a \cdot 3^b = y^n\)
• Möbius inversion formulas for flows of arithmetic semigroups
• Writing π as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers
• ON MACHIN'S FORMULA WITH POWERS OF THE GOLDEN SECTION
• The enhancement of Machin’s formula by Todd’s process
• Perfect Pell Powers
• Arctangent Formulas and Pi
• A new form of the Machin-like formula for pi by iteration with increasing integers
• On Arccotangent Relations for &#960
• A Problem on Arc Tangent Relations
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