Hungerbühler, Norbert Wasem, Micha <jats:title>Abstract</jats:title><jats:p>Given a real function <jats:italic>f</jats:italic> on an interval [<jats:italic>a</jats:italic>, <jats:italic>b</jats:italic>] satisfying mild regularity conditions, we determine the number of zeros of <jats:italic>f</jats:italic> by evaluating a certain integral. The integrand depends on <jats:italic>f</jats:italic>, <jats:italic>f</jats:italic>′ and <jats:italic>f</jats:italic>″. In particular, by approximating the integral with the trapezoidal rule on a fine enough grid, we can compute the number of zeros of <jats:italic>f</jats:italic> by evaluating finitely many values of <jats:italic>f</jats:italic>, <jats:italic>f</jats:italic>′ and <jats:italic>f</jats:italic>″. A variant of the integral even allows to determine the number of the zeros broken down by their multiplicity.</jats:p> application/pdf https://sonar.ch/global/documents/114192 eng info:eu-repo/semantics/altIdentifier/doi/10.1515/math-2018-0131 info:eu-repo/semantics/altIdentifier/issn/2391-5455 info:eu-repo/semantics/openAccess Open Mathematics. - Walter de Gruyter GmbH. - 2018, vol. 16, no. 1, p. 1621-1633 An integral that counts the zeros of a function http://purl.org/coar/resource_type/c_6501