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Some results on the gamma function for negative integers


Fisher, Brian and Kilicman, Adem (2012) Some results on the gamma function for negative integers. Applied Mathematics & Information Sciences, 6 (2). pp. 173-176. ISSN 1935-0090; ESSN: 2325-0399


The Gamma function Γ (s)(-r) is defined by Γ (s)(-r) = N - lim ε→0 ∫ε ∞ t -r-1, ln s t e -t dt for r, s = 0, 1, 2, . . . , where N is the neutrix having domain N′ = {ε : 0 < ε < ∞} with negligible functions finite linear sums of the functions ε λ ln s-1 ε, ln s ε : λ < 0, s = 1, 2,. .. and all functions which converge to zero in the normal sense as CMMI9.-1.epsilon1 tends to zero. In the classical sense Gamma functions is not defined for the negative integer. In this study, it is proved that for r = 1, 2,..., where φ(r) = Σ r i=1 1/i. Further results are also proved.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
Publisher: Natural Sciences Publishing
Keywords: Gamma function; Neutrix; Neutrix limit
Depositing User: Nur Farahin Ramli
Date Deposited: 26 Nov 2013 01:26
Last Modified: 26 Oct 2017 10:10
URI: http://psasir.upm.edu.my/id/eprint/25279
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