gives the arithmetic‐geometric mean of a and b.
- For certain special arguments, ArithmeticGeometricMean automatically evaluates to exact values.
- ArithmeticGeometricMean can be evaluated to arbitrary numerical precision.
- ArithmeticGeometricMean is a homogeneous function of a and b, and has a branch cut discontinuity in the complex plane, with a branch cut running from to 0.
- ArithmeticGeometricMean automatically threads over lists.
Examplesopen allclose all
Basic Examples (4)
Numerical Evaluation (4)
Specific Values (4)
Find a value of x for which ArithmeticGeometricMean[3,x]=1.5:
Plot the ArithmeticGeometricMean function for various orders:
Function Properties (4)
Series Expansions (2)
Find the Taylor expansion using Series:
Compare with ArithmeticGeometricMean:
Closed form of the iteration steps for calculating the arithmetic‐geometric mean expressed through ArithmeticGeometricMean: