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Wirtinger derivatives
In complex analysis of one and several complex variables, Wirtinger derivatives (sometimes also called Wirtinger operators〔See references and .〕), named after Wilhelm Wirtinger who introduced them in 1927 in the course of his studies on the theory of functions of several complex variables, are partial differential operators of the first order which behave in a very similar manner to the ordinary derivatives with respect to one real variable, when applied to holomorphic functions, antiholomorphic functions or simply differentiable functions on complex domains. These operators permit the construction of a differential calculus for such functions that is entirely analogous to the ordinary differential calculus for functions of real variables.〔Some of the basic properties of Wirtinger derivatives are the same ones as the properties characterizing the ordinary (or partial) derivatives and used for the construction of the usual differential calculus.〕
==Historical notes==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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