MATHEMATICA BOHEMICA, Vol. 128, No. 4, pp. 367-377 (2003)

On the incomplete gamma function and
the neutrix convolution

Brian Fisher, Biljana Jolevska-Tuneska, Arpad Takaci

B. Fisher, Department of Mathematics and Computer Science, Leicester University, Leicester, LE1 7RH, England, e-mail: fbr@le.ac.uk; B. Jolevska-Tuneska, Faculty of Electrical Engineering, Karpos II bb, Skopje, Republic of Macedonia, e-mail: biljanaj@etf.ukim.edu.mk; A. Takaci, Department of Mathematics, University of Novi Sad, Novi Sad, Yugoslavia, e-mail: takaci@im.ns.ac.yu

Abstract: The incomplete Gamma function $\gamma(\ab,x)$ and its associated functions $\gamma(\ab,x _+)$ and $\gamma(\ab,x _-)$ 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.

Keywords: Gamma function, incomplete Gamma function, convolution, neutrix convolution

Classification (MSC2000): 33B10, 46F10

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