LAPLACE TRANSFORM: Gamma Function

Let , with . Set . It is easy to see that F(s) is defined for s > 0. Consider the new variable r = st. Then we have

,

which implies

,

where the Gamma function is defined by

The domain of the Gamma function is x > 1. Using integration by part, one can easily prove the fundamental formula

,

which implies (knowing that )

Consequently, we have

If you are interested to learn more about the Gamma function, click HERE.

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