2013/03/10 by Jacopo D’Aurizio, Jacopo D'Aurizio, D'Aurizio, Jacopo
Mathematics · #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Number Theory (math.NT) #math.CA #math.NT
paper · pdf · doi:10.48550/arxiv.1304.0753
arxiv created 2013/03/10 · openalex publication_date 2013/03/10 · arxiv updated 2013/04/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this article we show a tecnique based on the Weierstrass product for the sine and cosine function and the bisection formula for the cotangent function that leads to a generalization of the classical Shafer-Fink inequality (3 x)/(1+2√(1+x2)) < \arctan x < (πx)/(1+2√(1+x2)). Other algebraic approximations are also shown, including one that follows from the Chebyshev expansion for the arctangent function in the interval [-1,1].