Volume of the n-ball? Generally, what I would consider the defining equation for pi. Has no factor of 2? V_n = pi^(n/2)R^n / Gamma(n/2+1) = C_n R^n C_n = pi

Volume of the n-ball? Generally, what I would consider the defining equation for pi. Has no factor of 2? V_n = pi^(n/2)R^n / Gamma(n/2+1) = C_n R^n C_n = pi^k/k! for even n=2k C_n = 2^(k+1)k!pi^k / (2k+1)! for odd n=2k+1 Of course we could just change the definition of gamma, but I prefer gamma as an extension of factorial.