Question: Prove that the gamma function G(a)= R 0 xa????1e????x dx, a >0 fulfills the equalities G(1) = 1, G(1=2) = p p, and G(a

Prove that the gamma function G(a)=

R ¥

0 xa????1e????x dx, a >0 fulfills the equalities G(1) = 1, G(1=2) =

p p, and G(a +1) = aG

(a) for any a > 0. Deduce the two formulas

(2p+1)(2p-1)...1 T(p+1) p! and (p+3/2)= 2P+1 for pN.

(2p+1)(2p-1)...1 T(p+1) p! and (p+3/2)= 2P+1 for pN.

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