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Homework Statement
Show that the series,
[tex]\sum_{n=1}^{\infty}\frac{1}{x^2+n^2}[/tex]
defines a continuous function f on the domain of convergence. What is this domain? In addition, write a series representation of ( f ' ) and determine the domain of convergence of this series to ( f ' ).
Homework Equations
The Attempt at a Solution
I need abit of help with this problem. If somebody could point me in the direction I would be very happy.
It looks to me that the series in question might be smaller than the series 1/ (k^2) and therefore converges on a domain of all real numbers.
I had a question about the wording, "the series defines a continuous function f on the domain of convergence". Does this mean that I am looking for the function that this series uniformly or pointwise converges to?