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Incomplete gamma function question

  1. Jul 3, 2009 #1
    I need to show whether or not:

    |[tex]\gamma[/tex](s,1)| converges for 0<Re(s)<1.

    Does anyone know of an expansion for this that would prove convergence?
     
  2. jcsd
  3. Jul 3, 2009 #2

    HallsofIvy

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    What do you mean by "converges"? There is no limit here.
     
  4. Jul 3, 2009 #3
    The improper integral
    [tex]\Gamma \left( a,z \right) =\int _{z}^{\infty }\!{{\rm e}^{-t}}{t}^{a-
    1}{dt}[/tex]
    converges for Re(a) > 0 by comparison with
    [tex]\int _{z}^{\infty }{t}^{a-1}{dt}[/tex].
    Is that the question?
     
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