I was researching the gamma function and then I stumbled into this: $$\Gamma(x)=\frac{e^{-\gamma x}}{x}\prod_{i\geq1}{\frac{e^{x/i}}{1+x/i}}$$ Turns out it's related to Weierstrass' Factorization Theorem. I've seen this before in: $$\sin(x)=x(1-\frac{x}{\pi})(1+\frac{x}{\pi})(1-\frac{x}{2\pi})(1+\frac{x}{2\pi})\dotsb$$ Figured now would be a good time to understand this theorem. Someone please help with a derivation of the theorem as well as how it connects to the product for the Gamma function for someone who is an undergraduate freshman (currently doing multivariable). Thanks
2026-04-01 22:34:48.1775082888
What is an elementary proof of the Weierstrass Factorization Theorem?
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