(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 ' ).

2. Relevant equations

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Series of functions help.

**Physics Forums | Science Articles, Homework Help, Discussion**