On defining the incomplete gamma function
The incomplete Gamma function γ(α, x+) is defined as locally summable function on the real line for α > 0 by γ(α,x+)= ∫0x+ uα-1e-udu, the integral diverging for α ≤ 0. The incomplete Gamma function can be defined as a distribution for α< 0 and α ≠ -1, - 2,... by using the recurrence formula γ(...
| Main Authors: | , , |
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| Format: | Article |
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Taylor and Francis Group
2003
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| Online Access: | http://psasir.upm.edu.my/id/eprint/112985/ |
| _version_ | 1848866096002629632 |
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| author | Fisher, Brian Jolevsaka-Tuneska, Biljana KiliÇman, Adem |
| author_facet | Fisher, Brian Jolevsaka-Tuneska, Biljana KiliÇman, Adem |
| author_sort | Fisher, Brian |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The incomplete Gamma function γ(α, x+) is defined as locally summable function on the real line for α > 0 by γ(α,x+)= ∫0x+ uα-1e-udu, the integral diverging for α ≤ 0. The incomplete Gamma function can be defined as a distribution for α< 0 and α ≠ -1, - 2,... by using the recurrence formula γ(α + 1, x+) = αγ(α x+) - x+αe-x. In the following, we define the distribution γ(-m, x+) for m = 0, 1, 2, .... |
| first_indexed | 2025-11-15T14:15:10Z |
| format | Article |
| id | upm-112985 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T14:15:10Z |
| publishDate | 2003 |
| publisher | Taylor and Francis Group |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1129852025-01-13T01:37:49Z http://psasir.upm.edu.my/id/eprint/112985/ On defining the incomplete gamma function Fisher, Brian Jolevsaka-Tuneska, Biljana KiliÇman, Adem The incomplete Gamma function γ(α, x+) is defined as locally summable function on the real line for α > 0 by γ(α,x+)= ∫0x+ uα-1e-udu, the integral diverging for α ≤ 0. The incomplete Gamma function can be defined as a distribution for α< 0 and α ≠ -1, - 2,... by using the recurrence formula γ(α + 1, x+) = αγ(α x+) - x+αe-x. In the following, we define the distribution γ(-m, x+) for m = 0, 1, 2, .... Taylor and Francis Group 2003 Article PeerReviewed Fisher, Brian and Jolevsaka-Tuneska, Biljana and KiliÇman, Adem (2003) On defining the incomplete gamma function. Integral Transforms and Special Functions, 14 (4). pp. 293-299. ISSN 1065-2469; eISSN: 1476-8291 https://www.tandfonline.com/doi/abs/10.1080/1065246031000081667 10.1080/1065246031000081667 |
| spellingShingle | Fisher, Brian Jolevsaka-Tuneska, Biljana KiliÇman, Adem On defining the incomplete gamma function |
| title | On defining the incomplete gamma function |
| title_full | On defining the incomplete gamma function |
| title_fullStr | On defining the incomplete gamma function |
| title_full_unstemmed | On defining the incomplete gamma function |
| title_short | On defining the incomplete gamma function |
| title_sort | on defining the incomplete gamma function |
| url | http://psasir.upm.edu.my/id/eprint/112985/ http://psasir.upm.edu.my/id/eprint/112985/ http://psasir.upm.edu.my/id/eprint/112985/ |