Abstract
The concept of the generalized arithmetic-geometric mean (GAGM) embraces both the arithmetic-geometric mean (AGM) and the modified arithmetic-geometric mean (MAGM) as two special concepts. The GAGM is applied for attaining a unifying formula for calculating complete elliptic integrals (CEI), including those of the third kind, thereby providing a conceptual basis for their exploration and exact evaluation, bypassing typical troubles of common software in calculating CEI. Detailed clarifying examples are provided.
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