The value of Γ(5/2)Γ(7/2)Γ(5/2)Γ(7/2) is:a.45π/1645𝜋/16b.45π/245𝜋/2c.45π/3245𝜋/32d.45π/8

The question seems to be incomplete. Could you please provide the complete question?

The value of Γ(5/2)Γ(7/2)Γ(5/2)Γ(7/2) is given by the formula:

Γ(n+1/2) = √π * (n-1)!! / 2^n

where n!! is the double factorial of n.

Let's calculate Γ(5/2) and Γ(7/2) separately:

Γ(5/2) = √π * (5-1)!! / 2^5 = √π * 3!! / 32 = √π * 3 / 32

Γ(7/2) = √π * (7-1)!! / 2^7 = √π * 5!! / 128 = √π * 15 / 128

Now, we multiply these values together:

Γ(5/2)Γ(7/2)Γ(5/2)Γ(7/2) = (√π * 3 / 32) * (√π * 15 / 128) * (√π * 3 / 32) * (√π * 15 / 128)

= π^2 * 9 * 225 / (32^2 * 128^2)

= 45π/16

So, the correct answer is a. 45π/16.