Arithmetic geometric mean

A more elaborate example for a generator is its use for an iteration based on iteratively computing arithmetic and geometric means – the so-called AGM iteration, see [1]:

We demonstrate this iteration here in the context of computing elliptic integrals for determining the period of a mathematical pendulum.

When started with the values , the AGM iteration generates a sequence of numbers with the following (astonishing) property:

The integral on the right-hand side is called a complete elliptic integral of the first kind. We'll now proceed to compute this elliptic integral. We use a generator to describe the iteration:

def arithmetic_geometric_mean(a, b):
    """
    Generator for the arithmetic and geometric mean
    a, b initial values
    """ 
    while True:    # infinite loop
         a, b = (a+b)/2, sqrt(a*b)
         yield a, b

As the sequences  converge to the same...