2012/02/13 by Mark B. Villarino, Villarino, Mark B.
Engineering · Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Engineering Education and Pedagogy #Experimental and Theoretical Physics Studies #FOS: Mathematics #Scientific Research and Discoveries #math.CA
paper · pdf · doi:10.48550/arxiv.1202.2782
18 pages. Many improvements in exposition in the section on Gauss' proof and on Ingham's computations. A significant expansion in the section on complex multiplication and renormalization
openalex publication_date 2012/02/13 · arxiv created 2014/09/01 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a self-contained development of Gauss' Arithmetic-Geometric Mean (AGM) and the work of A.E. Ingham who obtained rigorous error bounds for the AGM approximations to the period of a simple pendulum