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...subsets]] of the half-plane <math> \Re (s) > 1 </math>. It thus defines a holomorphic function on this half-plane, and this can be extended by analytic continuation to a

...d]] function of <var>2n</var> [[real number|real]] [[variable]]s to be a [[Holomorphic function|holomorphic one]]. They are named after [[Augustin-Louis Cauchy]] and [[Ber

At base <math> b\!>\!1</math>, tetration is assumed to be a [[holomorphic function]], at least for positive values of the [[real part]] of its argument.

...discontinuity is called the ''cut'' of the logarithm. The logarithm is a [[holomorphic function]] on the complex plane except for the origin and the cut.