Re: How to find this summation analytically?
From: Roger Stafford (ellieandrogerxyzzy_at_mindspring.com.invalid)
Date: 02/04/05
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Date: Fri, 04 Feb 2005 19:39:41 GMT
In article <040220050905385955%edgar@math.ohio-state.edu.invalid>,
edgar@math.ohio-state.edu.invalid wrote:
> In article <cturo7$dto$1@news.Stanford.EDU>, lucy <losemind@yahoo.com>
> wrote:
> ........
> I see no reason to think there is a solution in terms of known
> functions.
> ........
> G. A. Edgar
-----------
If we call Lucy's function, f(z) = sum(1/(2^k+z), k from 1 to infinity, it
satisfies the equality f(2*z) = 1/2*(1/(1+z)) + f(z)), and therefore has
the power series expansion
f(z) = 1 - z/3 + z^2/7 - z^3/15 + ... + (-1)^n/(2^(n+1)-1)*z^n + ...
for abs(z) < 2. It is thus an actual analytic function, but so far I
haven't managed to match it to any known functions or combinations thereof
I can find in my books. You may be right.
-- (Remove "xyzzy" and ".invalid" to send me email.) Roger Stafford
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