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

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