A Constructive Study of Landau's Summability Theorem

A summability theorem of landau, which classically is a simple consequence of the uniform boundedness theorem, is examined within bishop-style constructive mathematics. it is shown that the original theorem is nonconstructive, and that a natural weakening of the theorem is constructively equivalent to ishihara's principle bd-n. the paper ends with a number of results that, while not as strong as landau's theorem, nevertheless contain positive computational information related to its conclusion.