Hello everyone I tried to find out the range of $\Gamma$ function but, I didn't .Can anyone please explain the range of $\Gamma$ i.e. the minimum and maximum value of $\Gamma(x)$ of any number $x$.
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Are you referring to https://en.wikipedia.org/wiki/Gamma_distribution, or which? – Matti P. Oct 08 '20 at 11:07
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No Sir i want to know range of Gamma , Are the range of gamma is (0,Inf) ? or any other interval.with explanation – Harikesh Oct 08 '20 at 11:12
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You are referring to the Gamma function (generalization of factorial)? – Jack LeGrüß Oct 08 '20 at 11:17
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It seems like multiple people are confused about what you exactly mean by "gamma". Can you link some material that defines what it means? – Matti P. Oct 08 '20 at 11:21
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1yes sir like we find gamma(4)=3!=6 , but i want to know ,what could be the gamma(any number), i.e. range of "Gamma". – Harikesh Oct 08 '20 at 11:25
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Ah, okay! The fact that you put "statistics" as a tag, confused me! – Matti P. Oct 08 '20 at 11:28
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Well, obviously since it's essentially the factorial, the gamma function has no upper bound. – Matti P. Oct 08 '20 at 11:29
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Okay, what about lower bound? – Harikesh Oct 08 '20 at 11:31
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1No lower bound if you consider negative values of $x$. See grphical representation here : https://en.wikipedia.org/wiki/Gamma_function. – Jean Marie Oct 08 '20 at 11:37
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Okay,then I can say values of gamma(Number) lies between (-Inf ,+Inf)? – Harikesh Oct 08 '20 at 11:39
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Presumably, you mean $\Gamma$ over the reals. That range is $\mathbb R\setminus\{0\}$.
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"I don't know this notation." $\mathbb R-{0}$ is another notation for what you've written as $\mathbb R\setminus{0}$. See Other than $\setminus$ and $-$, are there any other notations for the set-theoretic difference of sets? on MSE or the Relative Complement section of the Complement page on English Wikipedia for some discussion. – Mark S. Oct 08 '20 at 13:05
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