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On the Fresnel sine integral and the convolution. (English) Zbl 1026.33002
Summary: The Fresnel sine integral \(S(x)\), the Fresnel cosine integral \(C(x)\), and the associated functions \(S_{+}(x), S_{-}(x), C_{+}(x)\), and \(C_{-}(x)\) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel sine integral and its associated functions with \(x^{r}_{+}, x^r\) are evaluated.

MSC:
33B10 Exponential and trigonometric functions
46F10 Operations with distributions and generalized functions
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