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Question Number 141535 by mohammad17 last updated on 20/May/21

$$howcansolvethiswithbystepsplease$$$$\frac{\mathrm{\Gamma }\left(\frac{3}{2}\right)\mathrm{\Gamma }\left(\frac{7}{2}\right)}{2\mathrm{\Gamma }\left(5\right)}iwantsolutionstepbystep$$$$becauseiunderstandthis?$$$$$$

Commented by Dwaipayan Shikari last updated on 20/May/21

$$\mathrm{\Gamma }\left(\frac{3}{2}\right)=\mathrm{\Gamma }(\frac{1}{2}+1)=\frac{1}{2}\mathrm{\Gamma }\left(\frac{1}{2}\right)=\frac{\sqrt{\pi }}{2}$$$$\mathrm{\Gamma }\left(\frac{7}{2}\right)=\mathrm{\Gamma }(\frac{5}{2}+1)=\frac{5}{2}\mathrm{\Gamma }(\frac{3}{2}+1)=\frac{5}{2}.\frac{3}{2}\mathrm{\Gamma }(\frac{1}{2}+1)=\frac{5.3.1}{2^3}\mathrm{\Gamma }\left(\frac{1}{2}\right)=\frac{15\sqrt{\pi }}{8}$$$$\frac{\mathrm{\Gamma }\left(\frac{3}{2}\right)\mathrm{\Gamma }\left(\frac{7}{2}\right)}{2\mathrm{\Gamma }\left(5\right)}=\frac{15\pi }{32.4!}=\frac{3.5\pi }{3.256}=\frac{5\pi }{256}$$

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