Transforms of Discontinuous and Periodic Functions

Author: John J Weber III, PhD Corresponding Textbook Sections:

• Section 7.6 – Transforms of Discontinuous and Periodic Functions

Prerequisite Knowledge

Gamma Function

Definition: Gamma Function, $\Gamma (t)$

The gamma function is defined by $\displaystyle \Gamma (t)=\int_0^{\infty}{e^{-u}u^{t-1}\,du}$, $t>0$.

Properties of the Gamma Function

• $\displaystyle \Gamma (t+1)=t\Gamma (t)$
• $\displaystyle \Gamma (t+1)=t!$

Practice

Use the integral definition of the gamma function to evaluate:

1. $\displaystyle \Gamma (1)$
2. $\displaystyle \Gamma (2)$
3. $\displaystyle \Gamma (3)$

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Last Modified: Sunday, 8 November 2020 18:47 EDT