Laplace transform of power function
In the defining integral (http://planetmath.org/ImproperIntegral)
of the Laplace transform of the power function
, we make the substitution (http://planetmath.org/SubstitutionForIntegration) :
Here we have assumed that and . According to the definition of the gamma function, the last integral is equal to. Thus we obtain
(1) |
The special case gives the result
(2) |