Gamma function convergence of an integral

  • #1

Main Question or Discussion Point

##\Gamma(x)=\int^{\infty}_0 t^{x-1}e^{-t}dt## converge for ##x>0##. But it also converge for negative noninteger values. However many authors do not discuss that. Could you explain how do examine convergence for negative values of ##x##.
 

Answers and Replies

  • #2
107
35
I'm pretty sure it doesn't converge for negative noninteger values and that the formula is not applicable there. Use the recursive formula for the Gamma function instead to get those values.
 
  • #3
mathman
Science Advisor
7,821
433
There is a general concept called analytic continuation, where a function has a particular representation in some domain can be extended outside this domain.
 

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