Here "smooth" may be interpreted as "infinitely differentiable", but often is interpreted as "twice continuously differentiable" or "continuously differentiable" or even just "continuous", since these weaker statements may be strong enough for a given task. "Compactly supported" means "vanishes outside [ c , d ] for some c , d such that a < c < d < b "; but often a weaker statement suffices, assuming only that h (or h and a number of its derivatives) vanishes at the endpoints a , b ; in this case the closed interval [ a , b ] is used.