Question

find the value of gamma (1/2)​

Answer 1

Answer:

Step-by-step explanation:

The value of Gamma half is root of pi........

Answer 2

Concept Introduction:-

Gamma is a popular way to carry out multiplication in complex numbers.

Given Information:-

We have been given that gamma $(1/2)$

To Find:-

We have to find that the value of gamma $(1/2)$

Solution:-

According to the problem

$\Gamma\left(\frac{1}{2}\right)=\int_{t=0}^{+\infty} t^{\frac{1}{2}-1} e^{-t} d t=\int_{t=0}^{+\infty} \frac{e^{-t}}{\sqrt{t}} d t$

and with $y=\sqrt{t}, d y=\frac{d t}{2 \sqrt{t}}$, we get

$\Gamma\left(\frac{1}{2}\right)=2 \int_{y=0}^{+\infty} e^{-y^{2}} d y=\int_{y=-\infty}^{+\infty} e^{-y^{2}} d y=\sqrt{\pi}$

Final Answer:-

The value of gamma $(1/2)$ is $\sqrt{\pi}$.