Editing Incomplete gamma function (section)

======Branches======
In particular, a single-valued and holomorphic logarithm exists on any such sector D having its imaginary part bound to the range {{open-open|''α'' − ''δ'', ''α'' + ''δ''}}. Based on such a restricted logarithm, {{math|''z''<sup>''s''</sup>}} and the incomplete gamma functions in turn collapse to single-valued, holomorphic functions on {{mvar|D}} (or {{math|'''C'''×''D''}}), called branches of their multi-valued counterparts on D. Adding a multiple of {{math|2''π''}} to {{mvar|α}} yields a different set of correlated branches on the same set {{mvar|D}}. However, in any given context here, {{mvar|α}} is assumed fixed and all branches involved are associated to it. If {{math|{{abs|''α''}} < ''δ''}}, the branches are called [[principal branch|principal]], because they equal their real analogues on the positive real axis. Note: In many applications and texts, formulas hold only for principal branches.