I was doing exercises for ahlfors's Complex Analysis book and came across the following problem $$(2π)^{\frac{n－1}{2}}\Gamma(z)＝n^{z－\frac{1}{2}}\Gamma(\frac{z}{n})\Gamma(\frac{z＋1}{n})...\Gamma(\frac{z＋n－1}{n})$$ I'm going to move the right side to the left side and use the formula for $\frac{1}{\Gamma(z)}$And then I put in $\frac{z}{n}$, $\frac{z＋1}{n}$and so on,But in the end, I found that the more and more complicated the formula, I realized that maybe my starting point is wrong, but I can't think of a better way to do this problem, so who can give me a little help
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Check this: https://math.stackexchange.com/q/752895/42969 – Martin R Sep 15 '23 at 08:10
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(Note that you are using non-standard plus and minus characters in the formula, that's why it is displayed so badly.) – Martin R Sep 15 '23 at 08:12