Talk:Mittag-Leffler Expansion for Cotangent Function

Logarithm of Product does not suffice. Neither does Logarithm of Infinite Product of Complex Functions. What you really need is Logarithmic Derivative of Infinite Product of Analytic Functions. (Note how the proof secretly uses logarithmtic derivatives, not derivatives of logarithms, because those aren't even continuous.) --barto (talk) (contribs) 16:49, 18 November 2017 (EST)
 * Voilà, hope you don't mind. It only remains to establish the locally uniform convergence, but this isn't hard, because it's even absolute, see Definition:Local Uniform Absolute Convergence of Product: it reduces to series. --barto (talk) (contribs) 17:10, 18 November 2017 (EST)
 * Not at all. I'm just unsure about a few things (this is purely to add to my own knowledge, I'm not questioning anything you're saying, you're far more versed in this than me :p) Why doesn't the second one suffice? Had I known it existed, I probably would've used that instead. I would've thought that convergence of the sum directly follows from the convergence of the product which is given in the theorem, though on second thought that might require a bit more explanation. I'm confused by your comment in brackets, can you explain a bit more? Caliburn (talk) 17:27, 18 November 2017 (EST)