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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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Main Authors:	Fisher, Brian, Jolevsaka-Tuneska, Biljana, KiliÇman, Adem
Format:	Article
Published:	Taylor and Francis Group 2003
Online Access:	http://psasir.upm.edu.my/id/eprint/112985/ https://www.tandfonline.com/doi/abs/10.1080/1065246031000081667
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id	my.upm.eprints.112985
record_format	eprints
spelling	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
institution	Universiti Putra Malaysia
building	UPM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Putra Malaysia
content_source	UPM Institutional Repository
url_provider	http://psasir.upm.edu.my/
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, ....
format	Article
author	Fisher, Brian Jolevsaka-Tuneska, Biljana KiliÇman, Adem
spellingShingle	Fisher, Brian Jolevsaka-Tuneska, Biljana KiliÇman, Adem On defining the incomplete gamma function
author_facet	Fisher, Brian Jolevsaka-Tuneska, Biljana KiliÇman, Adem
author_sort	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
_version_	1821107998932598784
score	13.244413

On defining the incomplete gamma function

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