\[I_d=\int_0^\infty d\mu\sqrt{\pi}\Gamma\left(\dfrac{d-1}{2}\right)\dfrac{_0F_1\left(\frac{d}{2},-\frac{\mu^2}{4}\right)}{\Gamma\left(\dfrac{d}{2}\right)}\mu^{d-3}=2^{d-3}\sqrt{\pi}\Gamma\left(\dfrac{d-2}{2}\right)\Gamma\left(\dfrac{d-1}{2}\right)\]