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valsi 
cnanlagau 
type 
fu'ivla 
creator 
krtisfranks 
time entered 
Sun Apr 1 01:47:34 2018 
Examples


English


Definition #70581
 Preferred
[edit]


definition 
x_{1} is the generalized arithmeticgeometric mean of the elements of the 2element set x_{2} (set; cardinality must be 2) of order x_{3} (either single extendedreal number xor an unordered pair/2element set of extendedreal numbers). 
notes 
Elements of x_{2} must have the same units/dimensionality; the result has the same units/dimensionality as them. If x_{3} = p for a single extendedreal number p, then
x_{3} = (p, p  1) also. If
x_{3} = (p, q) then the algorithm uses the pthpower mean (cnanfadi) and the qthpower mean; thus
x_{3} = (1, 0) corresponds to the standard arithmeticgeometric mean,
x_{3} = (0,  1) corresponds to the geometricharmonic mean. A poor choice of x_{3} will lead to nonconvergence of the sequences produced by the algorithm and, thus, leave x_{1} undefined (NAN error). x_{1} is the value to which each of the sequences produced by the algorithm converge (iff these values are mutually equal). Let M_{i} denote the unweighted ithpower mean for all i and let
x_{2} = (a_{0}, g_{0}),
x_{3} = (p, q); then the algorithm produces potentially infinite sequences
a = (a_{0}, a_{1},...), g = (g_{0}, g_{1},...), where
a_{n} = M_{p}(a_{(n1)}, g_{(n1)}), g_{n} = M_{q}(a_{(n1)}, g_{(n1)}) for all positive integers n. Notice that this word is symmetric (x_{1} remains constant and none of the sumti change in meaning) under an internal permutation of the elements/entries of x_{2} and/or of x_{3} (when taken as a pair or set), separately. See also: gau'i'o.

gloss words 

created by 
krtisfranks 
vote information 
1

time 
Sun Apr 1 02:55:45 2018 



Examples



krtisfranks  {cnano} + "Lagrange" + "Gauss" + English "arithmeticgeometric" (given by the "ag").  [edit] 

