Tas, KenanFisher, Brian02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2016-04-272025-09-182016-04-272025-09-182007Fisher, B., Taş, K. (2007). Commutative convolution of functions and distributions. Integral Transforms & Special Functions, 18(10), 689-697. http://dx.doi.org/10.1080/106524606009359651065-24691476-8291https://doi.org/10.1080/10652460600935965https://hdl.handle.net/123456789/12733Tas, Kenan/0000-0001-8173-453XThe commutative convolution f * g of two distributions f and g in D' is defined as the limit of the sequence {(f tau(n)) * (g tau(n))}, provided the limit exists, where {tau(n)} is a certain sequence of functions tn in D converging to 1. It is proved that |x|(lambda) * (sgn x|x|(-lambda-1)) = pi[cot (pi lambda) - cosec(pi lambda)] sgn x|x|(0), for lambda not equal 0, +/- 1, +/- 2, ... , where B denotes the Beta function.eninfo:eu-repo/semantics/closedAccessDistributionDirac Delta FunctionConvolutionArticle10.1080/106524606009359652-s2.0-34748838991