On the sine integral and the convolution (Q1608185)

Here the sine integral \(Si(\lambda x)\), the cosine integral \(Ci (\lambda x)\) and their associated functions \(Si_+(\lambda x)\), \(Si_-(\lambda x)\), \(Ci_+(\lambda x)\), \(Ci_-(\lambda x)\) are defined as locally summable functions and on the real line. Some convolutions of these functions and \(\sin (\mu x)\), \(\sin_+ (\mu x)\) and \(\sin_- (\mu x)\) are also established.