arrangement of double sums
- From: "vsgdp" <cloud00769@xxxxxxxxx>
- Date: 28 Feb 2007 13:24:03 -0800
Def: Let f be a double sequence and let g be one-to-one from Z+ to Z+
X Z+. Let G be defined by:
G(n) = f(g(n))
Then g is said to be an arrangement of the double sequence into the
sequence G.
-------------------------
Does G have a term for each term in the double sequence? Or is G a
sequence that picks a subset of terms from the double sequence? To
clarify: we can represent a 4x4 matrix by a 16 element array. Is this
the infinite analog where we may the double sequence into a linear
sequence?
Also, does arrangements have anything to do with the following
problem:
Assume doubleSum( a(n)*x^(nm) ) converges absolutely for |x| < 1 with
sum S(x). Show
Sum( a(n) [x^n / (1 - x^n)] ) = S(x) for |x| < 1.
I was trying to find an arrangement so that I could use the fact that
if the double sum converges absolutely, then so does Sum( G(n) ).
.
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