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Elliptic Functions > ArithmeticGeometricMean[a,b] > Introduction to the Arithmetic‚ÄźGeometric Mean


The arithmetic-geometric mean appeared in the works of J. Landen (1771, 1775) and J.‐L. Lagrange (1784-1785) who defined it through the following quite‐natural limit procedure:

C. F. Gauss (1791–1799, 1800, 1876) continued to research this limit and in 1800 derived its representation through the hypergeometric function .