 Conversely a Tauberian final value theorem makes assumptions about the frequency-domain behaviour of formula_2 to calculate formula_11 (or formula_12) 
(see Abelian and Tauberian theorems for integral transforms).In the following statements, the notation 'formula_14' means that formula_15 approaches 0, whereas 'formula_16' means that formula_15 approaches 0 through the positive numbers.Suppose that every pole of formula_2 is either in the open left half plane or at the origin, and that formula_2 has at most a single pole at the origin.