Gamma function - Exercise set 1

This exercise set contains some solved exercises on the Gamma function. The theory needed to solve these exercises is introduced in the lecture entitled Gamma function.

Exercise 1.1

Compute the following ratio: [eq1]

Solution

We need to repeatedly apply the recursive formulato the numerator of the ratio: [eq3]

Exercise 1.2

Compute

Solution

We need to use the relation of the Gamma function to the factorial function: which for becomes: [eq6]

Exercise 1.3

Express the following integral in terms of the Gamma function:

Solution

This is accomplished as follows: [eq8] where in the last step we have just used the definition of Gamma function.

by Marco Taboga

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