Geodesic
On the incomplete gamma function and the neutrix convolution
Mathematica Bohemica, Tome 128 (2003) no. 4, pp. 367-377

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MR Zbl
The incomplete Gamma function $\gamma (\alpha ,x)$ and its associated functions $\gamma (\alpha ,x _+)$ and $\gamma (\alpha ,x _-)$ are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions $x^r$ and $x_-^r$ are then found.
The incomplete Gamma function $\gamma (\alpha ,x)$ and its associated functions $\gamma (\alpha ,x _+)$ and $\gamma (\alpha ,x _-)$ are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions $x^r$ and $x_-^r$ are then found.
DOI : 10.21136/MB.2003.134004
Classification : 33B10, 33B20, 46F10
Keywords: Gamma function; incomplete Gamma function; convolution; neutrix convolution 
Fisher, Brian; Jolevska-Tuneska, Biljana; Takači, Arpad. On the incomplete gamma function and the neutrix convolution. Mathematica Bohemica, Tome 128 (2003) no. 4, pp. 367-377. doi: 10.21136/MB.2003.134004
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[1] van der Corput, J. G.: Introduction to the neutrix calculus. J. Analyse Math. 7 (1959–60), 291–398. | MR

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

[3] Fisher, B., Yakubovich, S., Telci, M.: On the incomplete Gamma function, submitted for publication.

[4] Gel’fand, I. M., Shilov, G. E.: Generalized Functions, vol. I. Academic Press, 1964. | MR

[5] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G.: Higher Transcendental Functions, vol. I. McGraw-Hill, New York, 1953.

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