Nminimize[{(2^(2 x) Gamma[1/2 + x])/(Sqrt[\[Pi]] x^3 Gamma[x]) - 1/x^2, x>0}, x]Nminimize[{(2^(2 x) Gamma[1/2 + x])/(Sqrt[\[Pi]] x^3 Gamma[x]) - 1/x^2, x>0}, x]

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