# Possible rearrangments of double products containing sine function : [closed]

I know that the following question is not a fit (at all ) for this site , So , apologies ; but it interests me in very unusual way ; so I'm asking here . If not appropriate to post here tell me I'll delete it quickly.

I also posted this on MSE.[https://math.stackexchange.com/q/3532547/702232] with some upvotes but, no response for long time :

Consider the following 'function':

$$g(x)= \frac{\sin^2\pi x}{(\pi x)^2\left(1-x^2\right)^2} \prod_{n=2}^\infty \frac{\pi x}{n\sin\frac{\pi x}{n}}$$

Now consider the following products :

$$\prod_{k=2}^c (\frac{1}{1+\frac{k}{g(k)}} + \frac{1}{1+\frac{2c-k}{g(2c-k)}})$$

Or

$$\prod_{k=2}^c (\frac{1}{1+\frac{1}{g(k)}} + \frac{1}{1+\frac{1}{g(2c-k)}})$$

What are some possible (workable) Rearrangments of the above products ?

Note : Not a trivial function ; could have application to Goldbach Conjecture .

• As others (including me) have commented on your other questions, writing an expression and asking others to figure out how it could apply to problems like Goldbach—or what is a "possible (workable) Rearrangement", whatever that means—is far too broad, besides being not a well defined question, and does not belong here. – LSpice May 6 at 22:33