Formula:7143

Digital Library of Mathematical Functions ID 19.22.E9

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \frac{4}{\pi}\CarlsonsymellintRG@{0}{a_{0}^{2}}{g_{0}^{2}}=\frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right)=\frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right),}

Symbols List

• ${\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of second kind
• ${\displaystyle{\displaystyle M\left(\NVar{a},\NVar{g}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle a_{n}}}$: iterate
• ${\displaystyle{\displaystyle g_{n}}}$: iterate
 

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