Calculate the Gamma function Γ(2.7)

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\begin{align} \displaystyle Γ(2.7) &= \int_{0}^{∞} x^{(2.7-1)} \cdot e^{(-x)} dx \\[7pt] Γ(2.7) &= 1.54968 \end{align}

I got this answer online, but I do not know how to get it. Would you please explain how to get the value of this gamma function?

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See this article on the Gamma function from the Digital Library of Mathematical Functions. There's no simple way to compute values of the Gamma function by hand, but there are a number of ways to implement this in software and lots of software is already written for this task.

http://dlmf.nist.gov/5