GeometricMean

GeometricMean (a, b)

The GeometricMean function returns the arithmetic-geometric mean of two positive real numbers a and b. The mean is computed by creating two sequences {a_i} and {b_i} initialized to the input values: a₀=a and b₀=b with

$$\displaystyle a_{n+1}=\frac{1}{2}\left(a_{n}+b_{n}\right),$$ $$\displaystyle b_{n+1}=\sqrt{a_{n} b_{n}} .$$

The two sequences converge in a few iterations to a single value which is the arithmetic-geometric mean.

See Also

EllipticK, EllipticE