in the first image, I don't understand how i'm supposed to get those two terms. and for the second image, i don't understand how I'm supposed to get this equation.
thanks in advance
in the first image, I don't understand how i'm supposed to get those two terms. and for the second image, i don't understand how I'm supposed to get this equation.
thanks in advance
In the first image, the term $\displaystyle \frac{\sin\theta}r\frac{\cos\theta}r\partial_\thet a$ seems to have been added and then subtracted, in one line of the calculation, for no reason whatever. Those terms don't appear in either the previous line or the following line of the calculation, and the whole thing would be improved if you just wipe them out.
In the second image, if $\displaystyle S_N(\theta) = \sum_{n=-N}^Ne^{in\theta}$ then $\displaystyle e^{i\theta}S_N(\theta) = \sum_{n=-N}^Ne^{i(n+1)\theta}$. This is the same as the sum defining $\displaystyle S_N(\theta)$, except that the first term has been dropped, and one term has been added at the end.