Editing Incomplete gamma function (section)

=====Behavior near branch point=====
The decomposition above further shows, that γ behaves near {{math|1=''z'' = 0}} [[asymptotic]]ally like:
<math display="block">\gamma(s, z) \asymp z^s \, \Gamma(s) \, \gamma^*(s, 0) = z^s \, \Gamma(s)/\Gamma(s+1) = z^s/s.</math>

For positive real {{mvar|x}}, {{mvar|y}} and {{mvar|s}}, {{math|''x''<sup>''y''</sup>/y → 0}}, when {{math|(''x'', ''y'') → (0, ''s'')}}. This seems to justify setting {{math|1=''γ''(''s'', 0) = 0}} for real {{math|''s'' > 0}}. However, matters are somewhat different in the complex realm. Only if (a) the real part of {{mvar|s}} is positive, and (b) values {{math|''u''<sup>''v''</sup>}} are taken from just a finite set of branches, they are guaranteed to converge to zero as {{math|(''u'', ''v'') → (0, ''s'')}}, and so does {{math|''γ''(''u'', ''v'')}}. On a single [[branch point|branch]] of {{math|''γ''(''b'')}} is naturally fulfilled, so '''there''' {{math|1=''γ''(''s'', 0) = 0}} for {{mvar|s}} with positive real part is a [[Continuous function|continuous limit]]. Also note that such a continuation is by no means an [[analytic continuation|analytic one]].