Citation
Fisher, Brian and Kilicman, Adem
(2012)
Some results on the gamma function for negative integers.
Applied Mathematics & Information Sciences, 6 (2).
pp. 173176.
ISSN 19350090; ESSN: 23250399
Abstract
The Gamma function Γ (s)(r) is defined by Γ (s)(r) = N  lim ε→0 ∫ε ∞ t r1, 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 s1 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 
Statistic Details:  View Download Statistic 
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