An Application of Neutrix Calculus to Modified Degenerate Gamma Function

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DOI: https://doi.org/10.28924/2291-8639-24-2026-45
Published: Feb 19, 2026
Cite as:
Inci Ege, An Application of Neutrix Calculus to Modified Degenerate Gamma Function, Int. J. Anal. Appl., 24 (2026), 45.

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Inci Ege

Abstract

The modified degenerate Gamma function \(\Gamma^{*}\lambda(x)\) is defined for positive values of x; however, it is not defined for zero or negative values of \(x\). In this study, the concepts of neutrix and neutrix limit are employed to extend the definition of the modified degenerate Gamma function \(\Gamma^{*}\lambda(x)\) for all real values of \(x\). The results demonstrate that the established definitions and findings recover the classical results for Euler’s Gamma function \(\Gamma(x)\) as \(\lambda \rightarrow 0\) for all real values of \(x\). Additionally, explicit equations for \(\Gamma^{*}\lambda(0)\) and \(\Gamma^{*}_\lambda(-n)\), where n is a positive integer, are given.

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