Chapter A, Problem 1E

To determine

The quantity $\Gamma \left(6\right)$ using Gamma Function.

Answer to Problem 1E

The value of $\Gamma \left(6\right)$ is $\underset{\_}{120}$.

Explanation of Solution

Given:

The quantity is $\Gamma \left(6\right)$.

Calculation:

The quantity is $\Gamma \left(6\right)$.

It is known that, the value of gamma function for any positive whole number $n$ is given as $\Gamma n=\left(n-1\right)!$.

It is given that, the value of $n$ is $6$.

The value of $\Gamma \left(6\right)$ is calculated as follows.

$\begin{array}{c}\Gamma \left(6\right)=\left(6-1\right)!\\ =5!\\ =5\times 4\times 3\times 2\times 1\\ =120\end{array}$

Thus, the value of $\Gamma \left(6\right)$ is $\underset{\_}{120}$.