Combinatorics and Graph Theory

    

On the Euler Integral for the Positive and Negative Factorial

Authors: Tai-Choon Yoon, Yina Yoon

We reviewed the Euler integral for the factorial, Gauss' Pi function, Legendre's gamma function and beta function, and found that gamma function is defective in $\Gamma(0)$ and $\Gamma(-x)$ because they are undefined or indefinable. And we came to a conclusion that the definition of a negative factorial, that covers the domain of the negative space, is needed to the Euler integral for the factorial, as well as the Euler $Y$ function and the Euler $Z$ function, that supersede Legendre's gamma function and beta function.

Comments: 10 Pages. [Heading "Abstract" added by viXra Admin]

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Submission history

[v1] 2020-12-18 20:40:38

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