Question

what is the value of gamma 5/2 ?​

Answer 1

8.√π/15

Step-by-step explanation:

Using Gamma(x+1) = x Gamma(x), we get

(√π)=Gamma(1/2) = Gamma{(-1/2)+1) =

(-1/2)Gamma(-1/2) = (-1/2)Gamma{(-3/2)+1} =

(-1/2)(-3/2)Gamma(-3/2)

=(-1/2)(-3/2)Gamma{(-5/2)+1}

= (-1/2)(-3/2)(-5/2)Gamma(-5/2)

= (-15/8)Gamma(-5/2).

Therefore Gamma(-5/2) = -8.√π/15.

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Answer 2

Answer:

The value of gamma $5/2$ is $\frac{3}{4} \sqrt{\pi}$.

Step-by-step explanation:

We are asked to find the value of gamma $5/2$.

To identify Gamma function.

$\Gamma(s)=(s-1) !$

Where,

$s$: Positive Integer

To identify Gamma function for other integers:

$r(s)=\int_{0}^{\infty} t^{s-1} e^{-t} d t$,

This can be further simplified as follows:

$\Gamma(s)=(s-1) \Gamma(s-1)$

Where,

$s$: positive real number and $s$ should always be greater than $0$.

Apply the simplified version of the second formula:

$\Gamma(5 / 2)=(s-1) \Gamma(s-1)$

$\begin{aligned}&\Gamma(5 / 2)=((5 / 2)-1) \Gamma((5 / 2)-1) \\&\Gamma(5 / 2)=(3 / 2) \Gamma(3 / 2)\end{aligned}$

Now we will calculate $\Gamma(3 / 2)$:

Using $\Gamma(n+1)=n \Gamma(n)$

We can rearrange for $\Gamma(n)$

To get $\Gamma(n)=\frac{1}{n} \Gamma(n+1)$

Then using $n=\frac{3}{2}$, after substituting, we have:

$\Gamma(3 / 2)=\Gamma(1 / 2+1)=\frac{1}{2} \Gamma(1 / 2)=\frac{1}{2} \sqrt{\pi}$

$\Gamma(5 / 2)=(3 / 2) \Gamma(3 / 2)$ and $\Gamma(3 / 2)=\frac{1}{2} \sqrt{\pi}$

$\Gamma(5 / 2)=\frac{3}{2}\times \frac{1}{2} \sqrt{\pi}\\\Gamma(5 / 2)=\frac{3}{4} \sqrt{\pi}$

Therefore, the required value of gamma is $\frac{3}{4} \sqrt{\pi}$.