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

Connections within the arithmetic-geometric mean group and with other function groups

Representations through more general functions

The arithmetic‐geometric mean can be represented through the reciprocal function of the particular cases of hypergeometric and Meijer G functions:

Representations through related equivalent functions

The definition of the arithmetic‐geometric mean can be interpreted as a representation of through related equivalent functions—the reciprocal of the complete elliptic integral with :