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Eurasian Math. J., 2019, Volume 10, Number 1, Pages 30–51 (Mi emj321)  

On the incomplete gamma function and its neutrix convolution for negative integers

M. Lina, B. Fisherb, S. Orankitjaroenc

a Institute of Technology of Cambodia, Russian Conf. Blvd, Phnom Penh, Cambodia
b University of Leicester, Leicester, LE1 7RH, U.K
c Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand

Abstract: We define the distributions $\gamma^+(-r,x)$ and $\gamma^-(-r,x)$ from the incomplete Gamma function $\gamma(-r,x)$ for negative integers. We then evaluate some convolutions and neutrix convolutions of these distributions and the functions $(x^s)_+$, $(x^s)_-$ and $x^s$.

Keywords and phrases: Gamma function, incomplete Gamma function, convolution, neutrix convolution.

DOI: https://doi.org/10.32523/2077-9879-2019-10-1-30-51

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Bibliographic databases:

MSC: 33B10, 46F10
Received: 02.12.2016
Revised: 11.03.2019
Language:

Citation: M. Lin, B. Fisher, S. Orankitjaroen, “On the incomplete gamma function and its neutrix convolution for negative integers”, Eurasian Math. J., 10:1 (2019), 30–51

Citation in format AMSBIB
\Bibitem{LinFisOra19}
\by M.~Lin, B.~Fisher, S.~Orankitjaroen
\paper On the incomplete gamma function and its neutrix convolution for negative integers
\jour Eurasian Math. J.
\yr 2019
\vol 10
\issue 1
\pages 30--51
\mathnet{http://mi.mathnet.ru/emj321}
\crossref{https://doi.org/10.32523/2077-9879-2019-10-1-30-51}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85066235261}


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