let Γ(x)=∫_0 ^∞ t^(x−1) e^(−t) dt 1) find Γ(x+1) interms of Γ(x) with x>0 2)calculate Γ(n) for n ∈ N^★ 3)calculate Γ((3/2)) .


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Question Number 33896 by math khazana by abdo last updated on 26/Apr/18

$l e t Γ (x) = \int_{0}^{\infty} t^{x - 1} e^{- t} d t$ $1) f i n d Γ (x + 1) i n t e r m s o f Γ (x) w i t h x > 0$ $2) c a l c u l a t e Γ (n) f o r n \in N^{★}$ $3) c a l c u l a t e Γ (\frac{3}{2}) .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 27/Apr/18

	$⌈ (3 / 2) = ⌈ (1 / 2 + 1)$ $= 1 / 2 ⌈ (1 / 2)$ $= 1 / 2 \sqrt{Π}$
	Answered by tanmay.chaudhury50@gmail.com last updated on 27/Apr/18

	$1 . ⌈ (x + 1) = x . ⌈ (x)$
	Answered by tanmay.chaudhury50@gmail.com last updated on 27/Apr/18

	$2 . ⌈ (n) = ⌈ (n - 1 + 1)$ $= (n - 1) ⌈ (n - 2)$ $= (n - 1) (n - 2) ⌈ (n - 3)$ $t h u s t h e v a l u e i s f a c t o r i a l (n - 1)$ $⌈ (n) = (n - 1)!$
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