General question about correct notation

[MarkoA]

Hi,

I have a question about how to write down the following problem in a thesis.

I have a standing sinusodial wave with amplitude:
$$|\hat{q}_n|$$
which I want to express as superposition of two traveling waves. Would you suggest do write the sum in the last line like I did, or has somebody a better idea?

$$\DeclareMathOperator{\e}{e} \begin{split} w &= |\hat{q}_n| \sin(n\pi x/L) \e^{i\omega t} \\ &= |\hat{q}_n| \frac{1}{2i}(\e^{i n \pi x/L} - \overline{\e^{i n \pi x/L}}) \e^{i\omega t} \\ &= |\hat{q}_n| \e^{i\omega t} \sum_{\nu = \pm n} \frac{\nu}{2i} \e^{i \nu \pi x/L} \; . \end{split}$$

Thanks!

 

[mfb]

I think I would just keep it as two separate terms. Where is the point of a sum symbol?