cnanlagau fu'ivla

x1 is the generalized arithmetic-geometric mean of the elements of the 2-element set x2 (set; cardinality must be 2) of order x3 (either single extended-real number xor an unordered pair/2-element set of extended-real numbers).

Elements of x2 must have the same units/dimensionality; the result has the same units/dimensionality as them. If x3=p for a single extended-real number p, then x3=(p,p-1) also. If x3 = (p,q) then the algorithm uses the pth-power mean (cnanfadi) and the qth-power mean; thus x3 = (1,0) corresponds to the standard arithmetic-geometric mean, x3 = (0, -1) corresponds to the geometric-harmonic mean. A poor choice of x3 will lead to non-convergence of the sequences produced by the algorithm and, thus, leave x1 undefined (NAN error). x1 is the value to which each of the sequences produced by the algorithm converge (iff these values are mutually equal). Let Mi denote the unweighted ith-power mean for all i and let x2 = (a0,g x3 = (p,q); then the algorithm produces potentially infinite sequences a = (a0, a= (g0, g, where an = Mp(a= Mq(a for all positive integers n. Notice that this word is symmetric (x1 remains constant and none of the sumti change in meaning) under an internal permutation of the elements/entries of x2 and/or of x3 (when taken as a pair or set), separately. See also: gau'i'o.

In notes:

gau'i'o (exp!)
digit/number: Gauss' arithmetic-geometric mean of 1 and √(2)=sqrt(2) constant G ≈ .8346268…