Question

find a value of r (5/2)​

Answer 1

Answer:

2.5

Step-by-step explanation:

5/2 -2.5 it is helpful for you

Answer 2

Question:

Find the value of  $\Gamma$(5/2).

Answer:

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

Concept:

Gamma function ($\Gamma$).

$\Gamma$(n+1) = n $\Gamma$(n)        if n>0

$\Gamma$(n) = $\Gamma$(n+1)/n        if n<0

Find:

The value of $\Gamma$ (5/2).

Solution:

5/2 can be written as (1+3/2).

∴ $\Gamma (\frac{5}{2} ) = \Gamma (\frac{3}{2} + 1)$

Here n = 3/2 which is greater than 0.

$\Gamma (\frac{5}{2} ) = \Gamma (\frac{3}{2} + 1)$

       $= \frac{3}{2} \ \Gamma (\frac{3}{2} )$            ------------------ (i)

Now, 3/2 can be written as (1/2 + 1).

$\Gamma$(3/2) = $\Gamma$(1/2 + 1)

Here n = 1/2 which is also greater than 0.

$\Gamma$(3/2) = $\Gamma$(1/2 + 1)

          = (1/2) $\Gamma$(1/2)

But $\Gamma$(1/2) = √π

∴ $\Gamma$(3/2) =  (1/2) × √π

             = √π/2

Putting the value of  $\Gamma$(3/2) in (i), we get

$\Gamma$(5/2) = (3/2)(√π/2)

           = $\frac{3\sqrt{\pi} }{4}$

Hence, the value of  $\Gamma$(5/2) is  $\frac{3\sqrt{\pi} }{4}$.

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