ABSTRACT
At the outset it must be reaffirmed that an upper bound for the error term of an asymptotic expansion cannot be safely inferred simply by inspection of the rate of numerical decrease of the terms in the series at the point of truncation.' Even in the case of a convergent power-series expansion this cannot be done: the tail has to be majorized analytically (often by a geometric progression) before final accuracy can be guaranteed. For a series that is merely known to be asymptotic, the situation is much worse. First, it is impossible to majorize the tail. Secondly, the series represents not one function but an infinite class, and the error term naturally depends on which particular member of the class we have in mind.
