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An inequality for integrals of the form \(\int_{x}^{\infty}f(t)e^{it}\;dt\). (English) Zbl 1339.26053

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 \(f(x)\).

MSC:

26D15 Inequalities for sums, series and integrals
26A48 Monotonic functions, generalizations
33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
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