Jameson, Graham J. O. An inequality for integrals of the form \(\int_{x}^{\infty}f(t)e^{it}\;dt\). (English) Zbl 1339.26053 J. Math. Inequal. 10, No. 2, 505-509 (2016). Summary: It is shown that for a completely monotonic function \(f\), the absolute value of \(\int_{x}^{\infty}f(t)e^{it}\;dt\) is not greater than \(f(x)\). Cited in 1 Document MSC: 26D15 Inequalities for sums, series and integrals 26A48 Monotonic functions, generalizations 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) Keywords:integral inequality; completely monotonic function; sine integral; Fresnel integral PDFBibTeX XMLCite \textit{G. J. O. Jameson}, J. Math. Inequal. 10, No. 2, 505--509 (2016; Zbl 1339.26053) Full Text: DOI