Incomplete gamma function question

rman144
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I need to show whether or not:

|\gamma(s,1)| converges for 0<Re(s)<1.

Does anyone know of an expansion for this that would prove convergence?
 
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What do you mean by "converges"? There is no limit here.
 
The improper integral
\Gamma \left( a,z \right) =\int _{z}^{\infty }\!{{\rm e}^{-t}}{t}^{a-<br /> 1}{dt}
converges for Re(a) > 0 by comparison with
\int _{z}^{\infty }{t}^{a-1}{dt}.
Is that the question?
 

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