Bouey, Colleen M.; Medina, Herbert A.; Meza, Erika A new series for \(\pi\) via polynomial approximations to arctangent. (English) Zbl 1275.41006 Involve 5, No. 4, 421-430 (2012). Summary: Using rational functions of the form \[ \left\{\frac{t^{12m}(t-(2-\sqrt3))^{12m}}{1+t^2}\right\}_{m\in\mathbb N} \] we produce a family of efficient polynomial approximations to arctangent on the interval \([0,2-\sqrt3]\), and hence, provide approximations to \(\pi\) via the identity \(\arctan(2-\sqrt3)=\pi/12\). We turn the approximations of \(\pi\) into a series that gives about 21 more decimal digits of accuracy with each successive term. Cited in 1 ReviewCited in 1 Document MSC: 41A10 Approximation by polynomials 26D05 Inequalities for trigonometric functions and polynomials Keywords:polynomial approximations to arctangent; approximations of \(\pi\); series for \(\pi\) PDFBibTeX XMLCite \textit{C. M. Bouey} et al., Involve 5, No. 4, 421--430 (2012; Zbl 1275.41006) Full Text: DOI