Given the expression for unit volume in n-1 dimention using Euler Gamma Function: $S_{n−1}=\frac{2π^{n/2}}{Γ(\frac n2)}$, I'd want to derive the expression for unit volume i n-dimentional space (which I found to be $S_n=\frac{π^{n/2}}{2Γ(\frac n2+1)}$). I cannot find the right steps to go from n-1 to n, because via standard Gamma Function transformations I get untransformable forms. How can you derive it?
2026-02-23 08:43:05.1771836185
Deriving volume of an n-ball given the expression for n-1 ball
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