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A Product of Nested Radicals for the AGM

Abstract The arithmetic-geometric mean of two positive numbers a and b (AGM (a, b)) is the common limit of two sequences generated by an iterative process. This has proven to be an important device for calculating numbers and function in recent years. In this paper, we derive an infinite product representation for the AGM. The factors of this product are nested radicals resembling Vieta's famous product for pi.