let-x-0-t-x-1-e-t-dt-1-find-x-1-interms-of-x-with-x-gt-0-2-calculate-n-for-n-N-3-calculate-3-2-

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)!