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

preprint2014arXivOpen access

In this paper the incomplete gamma function $γ(α,x)$ and its derivative is considered for negative values of $α$ and the incomplete gamma type function $γ_*(α,x_-)$ is introduced. Further the polygamma functions $ψ^{(n)}(x)$ are defined for negative integers via the neutrix setting.

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

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Defining Incomplete Gamma Type Function with Negative Arguments and Polygamma functions ψ(n)(−m)ψ^{(n)}(-m)ψ(n)(−m)

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