Editing Incomplete gamma function (section)

======''s'' complex======
This result extends to complex {{mvar|s}}. Assume first {{math|1 ≤ Re(''s'') ≤ 2}} and {{math|1 < ''a'' < ''b''}}. Then
<math display="block">\left|\gamma(s, b) - \gamma(s, a)\right| \le \int_a^b \left|t^{s-1}\right| e^{-t}\, dt = \int_a^b t^{\Re s-1} e^{-t}\, dt \le \int_a^b t e^{-t}\, dt</math>
where<ref>{{Cite web|url=https://dlmf.nist.gov/4.4|title=DLMF: §4.4 Special Values and Limits ‣ Logarithm, Exponential, Powers ‣ Chapter 4 Elementary Functions|website=dlmf.nist.gov}}</ref>
<math display="block">\left|z^s\right| = \left|z\right|^{\Re s} \, e^{-\Im s\arg z}</math>
has been used in the middle. Since the final integral becomes arbitrarily small if only {{mvar|a}} is large enough, {{math|''γ''(''s'', ''x'')}} converges uniformly for {{math|''x'' → ∞}} on the strip {{math|1 ≤ Re(s) ≤ 2}} towards a holomorphic function,<ref name="class notes" /> which must be Γ(s) because of the identity theorem. Taking the limit in the recurrence relation {{math|1=''γ''(''s'', ''x'') = (''s'' − 1) ''γ''(''s'' − 1, ''x'') − ''x''<sup>''s'' − 1</sup> ''e''<sup>−''x''</sup>}} and noting, that lim {{math|1=''x''<sup>''n''</sup> ''e''<sup>−''x''</sup> = 0}} for {{math|''x'' → ∞}} and all {{mvar|n}}, shows, that {{math|''γ''(''s'', ''x'')}} converges outside the strip, too, towards a function obeying the recurrence relation of the Γ-function. It follows
<math display="block">\Gamma(s) = \lim_{x \to \infty} \gamma(s, x)</math>
for all complex {{mvar|s}} not a non-positive integer, {{mvar|x}} real and {{math|''γ''}} principal.