Re: Convergence of series
- From: israel@xxxxxxxxxxx (Robert Israel)
- Date: 14 Jul 2006 01:37:14 GMT
In article <1152822852.224064.175430@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
David Sevilla <sevillad@xxxxxxxxx> wrote:
Hi,
I have the following power series, whose convergence I'd like to know:
f(q) := Sum_{n=1..infinity} sigma(n) * q^n = q + 3 q^2 + 4 q^3 + 7
q^4 + 6 q^5 + ...
where sigma is the usual divisor function: sigma(n) := sum of all
divisors of n.
None of the usual tests seems useful here, but the coefficients grow so
slowly that I'd say it converges well... any ideas?
Hint: sigma(n) <= sum_{j=1}^n j
Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
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- From: David Sevilla
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