Some results on the gamma function for negative integers

• Main Authors: Fisher, Brian, Kilicman, Adem
• Format: Article
• Language: English
• Published: Natural Sciences Publishing 2012
• Online Access: http://psasir.upm.edu.my/id/eprint/25279/1/Some%20results%20on%20the%20gamma%20function%20for%20negative%20integers.pdf; http://psasir.upm.edu.my/id/eprint/25279/; http://www.naturalspublishing.com/Article.asp?ArtcID=425

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...