General
The arithmeticgeometric mean appeared in the works of J. Landen (1771, 1775) and J.‐L. Lagrange (17841785) 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 .
