Geodesic
On the incomplete gamma function and its neutrix convolution for negative integers
Eurasian mathematical journal, Tome 10 (2019) no. 1, pp. 30-51.

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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 $x^s$. 
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M. Lin; B. Fisher; S. Orankitjaroen. On the incomplete gamma function and its neutrix convolution for negative integers. Eurasian mathematical journal, Tome 10 (2019) no. 1, pp. 30-51. http://geodesic.mathdoc.fr/item/EMJ_2019_10_1_a3/

[1] I.M. Gel'fand, G.E. Shilov, Generalized functions, v. I, Academic Press, 1964 | MR

[2] B. Fisher, “Neutrices and the convolution of distributions”, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat., 17 (1987), 119–135 | MR

[3] B. Fisher, B. Jolevska-Tuneska, A. Kiliçman, “On defining the incomplete gamma function”, Integral Transform and Special Functions, 14:4 (2003), 293–299 | DOI | MR | Zbl

[4] B. Fisher, A. Kiliçman, “Some results on the Gamma function for negative integers”, Appl. Math. Inf. Sci., 6:2 (2012), 173–176 | MR

[5] B. Fisher, Y. Kuribayashi, “Neutrices and the Gamma function”, J. Fac. Ed. Tottori Univ., 36:1–2 (1987), 1–7 | MR

[6] B. Fisher, B. Jolevska-Tuneska, A. Takaci, “On the incomplete Gamma function and the neutrix convolution”, Math. Bohemica, 4:128 (2003), 367–377 | MR | Zbl

[7] B. Fisher, “Some notes on distributions”, Math. Student., 48 (1980), 269–281 | MR

[8] B. Fisher, S. Yakubovich, M. Telci, “On the incomplete Gamma function”, Rad. Mat., 11:1 (2002), 37–47 | MR | Zbl

[9] M. Lin, B. Fisher, S. Orankitjaroen, “On the incomplete Gamma function”, Int. J. App. Math., 27:1 (2014), 31–43 | MR | Zbl

[10] I.N. Sneddon, Special functions of mathematical physics and chemistry, Oliver Boyd, 1956 | MR

[11] J.G. van der Corput, “Introduction to the neutrix calculus”, J. Analyse Math., 7 (1959–60), 291–398 | MR