- #1
Hyperreality
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By definite integral, gamma function can be defined as
[tex]\Gamma(z)= \int_{0}^{\infty} t^{z-1}e^{-t} dt[/tex]
I've learned 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?
[tex]\Gamma(z)= \int_{0}^{\infty} t^{z-1}e^{-t} dt[/tex]
I've learned 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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