The neutrix limit of the -Gamma function and its derivatives

The q -analogue of the gamma function Γ q ( x ) is defined for x > 0 , 0 < q < 1 . In this work the neutrix and neutrix limit are used to define the q -analogue of the gamma function and its derivatives for zero and negative integer values of x . We prove that the neutrix limit of the q -Gamma function and its derivatives exist for all values of x .