| Title:
|
On the incomplete gamma function and the neutrix convolution (English) |
| Author:
|
Fisher, Brian |
| Author:
|
Jolevska-Tuneska, Biljana |
| Author:
|
Takači, Arpad |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
367-377 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Gamma function |
| Keyword:
|
incomplete Gamma function |
| Keyword:
|
convolution |
| Keyword:
|
neutrix convolution |
| MSC:
|
33B10 |
| MSC:
|
33B20 |
| MSC:
|
46F10 |
| idZBL:
|
Zbl 1052.33001 |
| idMR:
|
MR2032474 |
| DOI:
|
10.21136/MB.2003.134004 |
| . |
| Date available:
|
2009-09-24T22:10:51Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134004 |
| . |
| Reference:
|
[1] van der Corput, J. G.: Introduction to the neutrix calculus.J. Analyse Math. 7 (1959–60), 291–398. MR 0124678 |
| Reference:
|
[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 |
| Reference:
|
[3] Fisher, B., Yakubovich, S., Telci, M.: On the incomplete Gamma function, submitted for publication.. |
| Reference:
|
[4] Gel’fand, I. M., Shilov, G. E.: Generalized Functions, vol. I.Academic Press, 1964. MR 0166596 |
| Reference:
|
[5] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G.: Higher Transcendental Functions, vol. I.McGraw-Hill, New York, 1953. |
| . |
