By definite integral, gamma function can be defined as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Gamma(z)= \int_{0}^{\infty} t^{z-1}e^{-t} dt[/tex]

I've learnt some properties of Gamma function but my lecturer didn't tell us the domain of Gamma function. (I'm assuming it is defined for all non-negative real numbers).

I thought of this problem a while ago:

We know that

[tex] \sum_{n=0}^\infty \frac{x^n}{n!} = \lim_{n\rightarrow\infty} (1+x/n)^n=e^1[/tex]

My question is, is there a numerical solution to

[tex]\int_{0}^{\infty}\frac{1}{x!} dx[/tex]

where x is an non-negative real number over a continuous interval in terms of gamma function?

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# Can Gamma Function be used to Integrate Factorials?

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