1-2-Use-Method-and-Formula-

Question Number 167419 by Bagus1003 last updated on 16/Mar/22

(\frac{1}{2})! = ?

U s e M e t h o d a n d F o r m u l a!!!!!!!!!

Commented by mkam last updated on 16/Mar/22

(\frac{1}{2})! = Γ (\frac{3}{2}) = \frac{1}{2} Γ (\frac{1}{2}) = \frac{\sqrt{π}}{2}

Answered by alephzero last updated on 16/Mar/22

n! = Γ (n + 1)

\Rightarrow (\frac{1}{2})! = Γ (\frac{3}{2}) = Γ (1 + \frac{1}{2})

Γ (n) Γ (n + \frac{1}{2}) = 2^{1 - 2 n} \sqrt{π} Γ (2 n)

Γ (\frac{3}{2}) = Γ (1) Γ (1 + \frac{1}{2}) = Γ (1 + \frac{1}{2})

= 2^{1 - 2} \sqrt{π} Γ (2) = \frac{\sqrt{π}}{2}