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In this paper the incomplete gamma function $\gamma(\alpha,x)$ and itsderivative is considered for negative values of $\alpha $ and the incompletegamma type function $\gamma_*(\alpha,x_-)$ is introduced. Further the polygammafunctions $\psi^{(n)}(x)$ are defined for negative integers via the neutrixsetting.

Defining Incomplete Gamma Type Function with Negative Arguments and Polygamma functions $\psi^{(n)}(-m)$