Re: ancient math questions
- From: hagman <google@xxxxxxxxxxxxx>
- Date: Wed, 17 Oct 2007 05:18:09 -0700
On 16 Okt., 22:59, tommy1729 <tommy1...@xxxxxxxxx> wrote:
this question is one of the oldest in the history of math , and much studied between 200 - 1200 AC
yet i havent seen much more about it.
i must admit i am far from an expert on this kind of questions.
here it is:
sum [a_i] = sum [(a_i)^2]
now during the period 200 - 1200 AC "i" went from 1 to "a" , where "a" was a finite number , and this problem is not so hard.
however later calculus came and so we had infinite series.
so the question becomes again
sum [a_i] = sum [(a_i)^2]
but this time as an infinite series !
despite their being infinite possible solutions , we can restrict to the "beautifull cases" ; let a_i be f(i) and f is expressed in traditional functions.
Let f be *any* real-valued "traditional function" such that
both A := sum f(i) and B := sum [f(i)^2] converge.
Assume that A is not zero (then B is not zero either).
Then let a_i = A/B * f(i).
apart from ramanujan i am ignorant of any other mathematicians working on this...
I'm not sure if Ramanujan was awar of my result above.
hagman
i assume the idea is not new.
if it turns out to be so afterall , this is called a
"tommy series problem" ;-)
regards
tommy1729
.
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