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4. Let Ad and Vd denote the area and volume of the unit sphere and unit ball in Rd , respectively. (a) Prove the formula so that A2 = 2π, A3 = 4π, A4 = 2π2 ,.... Here Γ( is the Gamma function. [Hint: Use polar coordinates and the fact that ∫ 𝑒 −𝜋|𝑥| 2 𝑑𝑥 = 1. 𝑅𝑑 ] (b) Show that dVd = Ad, hence . In particular V2 = π, V3 = 4π/3,....

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Fourier Transformations Exercise
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