Allied & ICAR Exam Bank • ALLIED_1044 NAT • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Beta and Gamma functions

Question Statement:

The value of $\Gamma(5/2)$ is $k \sqrt{\pi}$. The decimal value of $k$ is:

Answer Key:

0.75

Step-by-Step Solution & Explanation

$\Gamma(n+1) = n \Gamma(n)$. $\Gamma(5/2) = \frac{3}{2} \Gamma(3/2) = \frac{3}{2} \times \frac{1}{2} \Gamma(1/2) = \frac{3}{4} \sqrt{\pi} = 0.75 \sqrt{\pi}$. Thus $k = 0.75$.
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