On the composition of the distributions x-1 ln| x | and x r+

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Fisher B., TAŞ K.

Integral Transforms and Special Functions, vol.16, no.7, pp.533-543, 2005 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 16 Issue: 7
• Publication Date: 2005
• Doi Number: 10.1080/10652460500105438
• Journal Name: Integral Transforms and Special Functions
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.533-543
• Keywords: Composition of distributions, Delta-function, Distribution, Neutrix, Neutrix limit
• Uşak University Affiliated: No

Abstract

Let F be a distribution and let f be a locally summable function. The distribution F( f )is defined as the neutrix limit of the sequence { F n( f )}, where Fn(x) = F(x)*δn(x) and {δn(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). The distribution (xr+)-1is ln |xr +|is evaluated for r = 1, 2, ....