Singularity function: Difference between revisions

Revision as of 17:56, 12 April 2012

Revision as of 17:57, 12 April 2012

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'''Singularity functions''' are a class of discontinues functions that contain [[Mathematical singularity|singularity]], i.e. they are discontinuous at its singular points. Singularity functions have been heavily studied in the field of mathematics under the alternative names of [[generalized functions]] and [[Distribution (mathematics)|distribution theory]]<ref>Distribution Theory and Transform Analysis, by A. H. Zemanian, New York: McGraw-Hill Book Company, 1965</ref><ref>Generalised Functions, Hoskins, Halsted Press, 1979</ref>. The functions are notated with brackets, as <math>\langle x-a\rangle ^n</math> where ''n'' is an integer. The "<math>\langle \rangle</math>" are often refereed as '''singularity brackets''' . The functions are defined as:

:{| class="wikitable"

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==References==

{{Reflist}}

==References==

*{{citation|first=A. H.|last=Zemanian|title=Distribution Theory and Transform Analysis|publisher=McGraw-Hill Book Company|year=1965}}.

*{{citation|first=R. F.|last=Hoskins|title=Generalised Functions|publisher=Halsted Press|year=1979}}.

*{{citation|first=M.J.|last=Lighthill|title=Fourier Analysis and Generalized Functions|publisher=Cambridge University Press|year=1958}}.

==External links==