Question regarding gamma function

  • #1
Denver Dang
148
1

Homework Statement


I have a quick question about the gamma function.

According to my textbook it says:
[tex]\int_{0}^{\infty }{{{x}^{n}}{{e}^{-ax}}dx}=\frac{\Gamma \left( n+1 \right)}{{{a}^{n+1}}}[/tex]
where [itex]\Gamma[/itex] is the gamma function. My question is, do n has to be an integer number, or can it also be a half-integer number for the gamma function to work ?

Thanks in advance.
 
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  • #2
Denver Dang said:

Homework Statement


I have a quick question about the gamma function.

According to my textbook it says:
[tex]\int_{0}^{\infty }{{{x}^{n}}{{e}^{-ax}}dx}=\frac{\Gamma \left( n+1 \right)}{{{a}^{n+1}}}[/tex]
where [itex]\Gamma[/itex] is the gamma function. My question is, do n has to be an integer number, or can it also be a half-integer number for the gamma function to work ?

Thanks in advance.

n is any real number > -1.
 
  • #3
Ok, thank you very much :)
 
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