I feel like this is a really simple question and that my brain is just not working.
I am looking at this paper and I am looking at the T matrix defined under equation 20. The author says that $A_{m,n}=\alpha_nD_{m-n}$. I am having trouble trying to figure out what the values of D are. I believe that they are the same as Equation 7, but with D(x) replacing a(x). Is this correct, or do I have to compute them on my own?
Look at Eq. (13), where the authors define
$$D(x) = \frac{a'(x)}{1+a'(x)^2}$$
where $a'(x) = (d/dx)a(x)$. The coefficients $D_m$ are defined as
$$D(x) = \sum_{m=-\infty}^{\infty} D_m e^{i m K x}$$
where $d=2 \pi/k$ is the period of the function $a$.
$D(x)$ is not the same as $a(x)$ by Eq. (13). The coefficients $D_m$ are given by
$$D_m = \frac{1}{d} \int_0^d dx \frac{a'(x)}{1+a'(x)^2} e^{-i m K x}$$