If the limit of a function f of x as x approaches infinity is finite, then it equals the limit as y approaches zero of y times this operation of the function f of y, according to the final value theorem.
If the limit of a function f of x as x approaches infinity is finite, then it equals the limit as y approaches zero of y times this operation of the function f of y, according to the final value theorem. A useful formula for calculating this operation applied to the product of the Heaviside step function times another function is given by the second-shifting property. This operation is always defined for a piecewise continuous function over the interval from zero to infinity by Lerch's theorem. In complex analysis, a function is analytic if the strip of convergence in the two-sided form of this operation has a finite width. In circuit analysis, it is common to convert ODE's with this operation into its moments, solve, and convert the result back into the time domain. For an input of one, this operation produces a value of one over s. For 10 points, name this integral transform which converts a function from its time domain into the s-domain. 
If the limit of a function f of x as x approaches infinity is finite, then it equals the limit as y approaches zero of y times this operation of the function f of y, according to the final value theorem.
Laplace transform