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(...
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Taylor and Francis Group
2003
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my.upm.eprints.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 |
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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, .... |
| format |
Article |
| author |
Fisher, Brian Jolevsaka-Tuneska, Biljana KiliÇman, Adem |
| spellingShingle |
Fisher, Brian Jolevsaka-Tuneska, Biljana KiliÇman, Adem On defining the incomplete gamma function |
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Fisher, Brian Jolevsaka-Tuneska, Biljana KiliÇman, Adem |
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Fisher, Brian |
| title |
On defining the incomplete gamma function |
| title_short |
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_sort |
on defining the incomplete gamma function |
| publisher |
Taylor and Francis Group |
| publishDate |
2003 |
| url |
http://psasir.upm.edu.my/id/eprint/112985/ https://www.tandfonline.com/doi/abs/10.1080/1065246031000081667 |
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1821107998932598784 |
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