Problem Statement

Write a function to compute the arithmetic-geometric mean of two numbers.

The arithmetic-geometric mean of two numbers can be (usefully) denoted as

a g m

( a , g )

{\displaystyle \mathrm {agm} (a,g)}

, and is equal to the limit of the sequence: Since the limit of

a

n

−

g

n

{\displaystyle a_{n}-g_{n}}

tends (rapidly) to zero with iterations, this is an efficient method. Demonstrate the function by calculating:

Let's start with the solution:

П1	<->	П0	1	ВП	8	/-/	П2	ИП0	ИП1
-	ИП2	-	/-/	x<0	31	ИП1	П3	ИП0	ИП1
*	КвКор	П1	ИП0	ИП3	+	2	/	П0	БП
08	ИП0	С/П