Arithmetic–geometric mean

Common card · No. 462893

In mathematics, the arithmetic–geometric mean (AGM or agM) of two positive real numbers x and y is the mutual limit of a sequence of arithmetic means and a sequence of geometric means. The arithmetic–geometric mean is used in fast algorithms for exponential, trigonometric functions, and other special functions, as well as some mathematical constants, in particular, computing π. The AGM is defined as the limit of the interdependent sequences a i {\displaystyle a_{i}} and g i {\displaystyle g_{i}} . Assuming x ≥ y ≥ 0 {\displaystyle x\geq y\geq 0} , we write: a 0...

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