Closed Form for Complex Gamma Function

In summary, there is no known closed form expression for ##\Gamma(\frac{1}{2}+ib)##, where ##b## is a real number. However, there is a Riemann-Siegel function that can approximate it. More information can be found on various platforms such as MathOverflow, Wikipedia, Stack Exchange, and Khan Academy. The formula for ##\Gamma(x)## is given by the integral $$\Gamma (x)=\int_0^{\infty}t^{x-1}e^{-t}dt$$ with additional resources for checking the LaTeX provided.
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  • #2
Hi, @thatboi, Wikipedia could be worth browsing?. Personally, Stack Exchange is too...Complex :smile:,for me.
Some other suggestions: Khan Academy. You've found the solution. This is the path:

$$\Gamma (x)=\int_0^{\infty}t^{x-1}e^{-t}dt$$

PF, please check the LaTeX.

Love, peace
 

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