Editing Incomplete gamma function (section)

=====Integral representation=====
The last relation tells us, that, for fixed {{mvar|s}}, {{mvar|γ}} is a [[Primitive function|primitive or antiderivative]] of the holomorphic function {{math|''z''<sup>''s''−1</sup> ''e''<sup>−''z''</sup>}}. Consequently, for any complex {{math|''u'', ''v'' ≠ 0}},
<math display="block">\int_u^v t^{s-1}\,e^{-t}\, dt = \gamma(s,v) - \gamma(s,u)</math>
holds, as long as the [[Line integral|path of integration]] is entirely contained in the domain of a branch of the integrand. If, additionally, the real part of {{mvar|s}} is positive, then the limit {{math|''γ''(''s'', ''u'') → 0}} for {{math|''u'' → 0}} applies, finally arriving at the complex integral definition of {{math|''γ''}}<ref name="auto3"/>
<math display="block">\gamma(s, z) = \int_0^z t^{s-1}\,e^{-t}\, dt, \, \Re(s) > 0. </math>

Any path of integration containing 0 only at its beginning, otherwise restricted to the domain of a branch of the integrand, is valid here, for example, the straight line connecting {{math|0}} and {{mvar|z}}.