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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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