I know what an arithmetic mean is and I also know what a geometric mean is, but could you define for me what an arithmetic geometric mean is ?
Hi,
I have a pair of known values that have the arithmetic geometric mean of
I have another pair of values which are unknown, but I do know that they have the same arithmetic geometric mean as the first two values, so that .
Is there any way to derive c and d from this info? Or at least to narrow down the possibilities of what c and d might be?
Thanks
I learned about it from here:
Arithmetic-geometric mean - Wikipedia, the free encyclopedia
i guess not since saying that the agm are equal is saying that the corresponding sequences have the same limit, but there are multiple different sequences which have the same limits.
for example if you have the sequence from (a,b) then you can find 2 numbers c and d such that they satisfy a_n=g_n for some n. so (c,d) will give rise to a sequence not equal to the first but has the same agm. but there may be many such iterations a_n and g_n.in this case (c,d) would give rise to a subsequence of the first.
Every sequence can be extended to another sequence.
eg
(1,1,1,1,1,1,.....)
is a subsequence of
(0,1,1,1,1,1,1,.....)
(........,1,1,1,1,.........)
is a subsequence of
(........,1,1,0,1,1,.........)
note the elements need not be integers