The so called back transformation or inverse Laplace transformation, i.e. the determination of the original function from the mapped function, is given by the inverse integral
for 
is valid. The variable 
must be
chosen such that the path of integration is in the convergence area along a line parallel
to the imaginary axis at distance from it, where must be
larger than the real parts of all singular values of 
.
It must be observed that Eq. (A.2) at a step location
delivers the arithmetic mean value of the left and
right limits
,
particularly for 
at the origin, as
.
