Incomplete gamma function question

**rman144** · Jul3-09, 12:05 PM

I need to show whether or not:

| $LaTeX Code: \\gamma$ (s,1)| converges for 0<Re(s)<1.

Does anyone know of an expansion for this that would prove convergence?

**HallsofIvy** · Jul3-09, 01:31 PM

What do you mean by "converges"? There is no limit here.

**g_edgar** · Jul3-09, 01:40 PM

The improper integral
$LaTeX Code: \\Gamma \\left( a,z \\right) =\\int _{z}^{\\infty }\\!{{\\rm e}^{-t}}{t}^{a-<BR>1}{dt}$
converges for Re(a) > 0 by comparison with
$LaTeX Code: \\int _{z}^{\\infty }{t}^{a-1}{dt}$ .
Is that the question?