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Keywords:
Gamma function; incomplete Gamma function; convolution; neutrix convolution
Gamma function; incomplete Gamma function; convolution; neutrix convolution
Summary:
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.
References:
[1] van der Corput, J. G.: Introduction to the neutrix calculus. J. Analyse Math. 7 (1959–60), 291–398. MR 0124678
[2] Fisher, B.: Neutrices and the convolution of distributions. Univ. u Novom Sadu Zb. Prirod.-Mat. Fak. Ser. Mat. 17 (1987), 119–135. MR 0939303
[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 0166596
[5] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G.: Higher Transcendental Functions, vol. I. McGraw-Hill, New York, 1953.
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