Abstract
In this chapter, we introduce the definitions and theorems for the Euler gamma function, Pochhammer symbols, and Euler beta function. We present the Weierstrass product, Legendre duplication formula, Weierstrass theorem, Winckler theorem, Stirling theorem, Hankel integral theorem, and Gauss multiplication formula. We also investigate the definitions of the incomplete gamma and beta functions. Finally, we report the logarithmic derivative of the gamma function.
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