The Undecidability of the Existence of Zeros of Real Elementary Functions

Abstract

From Richardson's undecidability results, it is shown that the predictive “there exists a real number r such that G(r) = 0” is recursively undecidable for G(x) in a class of functions which involves polynomials and the sine function. The deduction follows that the convergence of a class of improper integrals is recursively undecidable. © 1974, ACM. All rights reserved.