A family of high order approximations of Ramanujan type for perimeter of an ellipse

Jing-Feng Tian,Zhenhang Yang,Ming-Hu Ha,Hong-Jie Xing

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS（2021）

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摘要

Inspired by Ramanujan’s unusual approximations for the perimeter of an ellipse with semiaxis 1 and r∈( 0,1) , a family of approximations of Ramanujan type is constructed. We find the sharp lower and upper approximations have very high accuracy, and better than some known ones.

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关键词

Perimeter of an ellipse,Ramanujan type approximation,Complete integral of the second kind,Monotonicity,Inequality

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