I was struggling with this question, can use some help.
given that $a\not=0$ $$f_a(x) =\frac{1}{x^2+a^2}$$
I'm trying to find k and c dependent on a and b $$(f_a ∗ f_b) (x) = kf_c(x) $$
I know that the convolution can be written as $$ 2 \pi \hat f\hat g$$ but trying to make the calculation just leaves me in more trouble. I also tried directly calculating the convolution but i just hit an unsolvable integral.
Any ideas?