Talk:Sum over Integers of Sine of n + alpha of theta over n + alpha

This theorem does NOT work as written:

For $0 < \theta < 2 \pi$:

$\ds \sum_{n \mathop \in \Z} \dfrac {\map \sin {n + \alpha} \theta} {n + \alpha} = \pi$

for $\alpha \in \R$.

Counterexample:

$\ds \sum_{n \mathop \in \Z} \dfrac {\map \sin {n + 1} \pi} {n + 1} = 0$

To fix this, change the domain of $\theta$ to: For $0 < \theta < \pi$:

No wonder I am having such difficulty with this putrid subject if I can't even trust my fucking textbooks. :-(

Nothing I've ever done has ever worked out right. Probably time I retired. --prime mover (talk) 16:43, 16 March 2021 (UTC)

Nooooooo! You've got to stick around just to remind me that I'm really not that clever. When you say it, I almost believe you.  :) --Robkahn131 (talk) 17:05, 16 March 2021 (UTC)

It's also occurred to me that it can't work if $\alpha$ is an integer, because that would make $0$ on the bottom whenever $n = -\alpha$. So much for Ian Naisense Sneddon. --prime mover (talk) 17:21, 16 March 2021 (UTC)