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Simple asymptotic estimates for the perimeter of an ellipse using the Ivory series representation
Lampret, Vito
For the perimeter ▫$P(a,b)$▫ of an ellipse with the semi-axes ▫$a\geq b>0$▫, a sequence ▫$P_n(a,b)$▫ is constructed such that the relative error of the approximation ▫$P(a,b)\approx P_n(a,b)$▫ ...satisfies the following inequalities ▫$$0\leq \frac{P(a,b)-P_n(a,b)}{P(a,b)} \leq \frac{3}{\pi (2n+1)^3} \left(\frac{a-b}{a+b}\right)^{2n+2} \quad (n\in \mathbb{N}). $$▫
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