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## Main Question or Discussion Point

Hi,

I'm trying to prove that [tex]\lim_{x\to 0}\Gamma(x) = \infty[/tex] but I'm having a little trouble understanding.

Using the recurrence relation [tex]\Gamma(x)=\frac{\Gamma(x+1)}{x}[/tex] you can see that as the denominator tends towards zero, you'd expect the whole thing to get bigger and bigger...

but doesn't that mean that the numerator will get bigger and bigger as well because the next value of [itex]\Gamma(x)[/itex] will be bigger as well so it won't tend to infinity?

So how do you show this formally? Is there some mathematical was of quantifying how quickly the function tends towards infinity?

With many thanks,

Froskoy.

I'm trying to prove that [tex]\lim_{x\to 0}\Gamma(x) = \infty[/tex] but I'm having a little trouble understanding.

Using the recurrence relation [tex]\Gamma(x)=\frac{\Gamma(x+1)}{x}[/tex] you can see that as the denominator tends towards zero, you'd expect the whole thing to get bigger and bigger...

but doesn't that mean that the numerator will get bigger and bigger as well because the next value of [itex]\Gamma(x)[/itex] will be bigger as well so it won't tend to infinity?

So how do you show this formally? Is there some mathematical was of quantifying how quickly the function tends towards infinity?

With many thanks,

Froskoy.