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How to simplify SUM(k=0,inf,x^k/k!) ?
Message #1 Posted by Marcus von Cube, Germany on 11 Oct 2006, 4:37 a.m.

Hi

I'm playing around with various CAS implementations and found that it's no so easy to find the simplification for the well known infinite sum: 

 oo
----'
\     xk
 |   ---
/     k!
----'
 k=0
Is this possible with the 49g+ or any other Erable based CAS?

The Voyage 200 does not do it, while Derive on the PC knows the correct result.

Marcus

      
Re: How to simplify SUM(k=0,inf,x^k/k!) ?
Message #2 Posted by Crawl on 11 Oct 2006, 10:29 p.m.,
in response to message #1 by Marcus von Cube, Germany

I don't think the 49G+ can do it.

It can at least find sum(n = 1, inf, 1/n^x) for even x.

And it can find various closed forms of finite sums (the geometric series, 1 + 2 + 3 + ... + n = n(n+1)/2, sums of reciprocal triangle numbers, more complicated cases), too.

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