In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood...
24 KB (3,334 words) - 02:45, 20 August 2024
analysis, a complex-valued function f {\displaystyle f} of a complex variable z {\displaystyle z} : is said to be holomorphic at a point a {\displaystyle...
6 KB (1,136 words) - 23:43, 16 May 2023
heading. As in complex analysis of functions of one variable, which is the case n = 1, the functions studied are holomorphic or complex analytic so that, locally...
124 KB (17,658 words) - 20:14, 19 August 2024
analytic functions are exactly equivalent to holomorphic functions, and are thus much more easily characterized. For the case of an analytic function with...
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complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a set of isolated...
8 KB (1,114 words) - 00:40, 12 February 2024
antiholomorphic functions (also called antianalytic functions) are a family of functions closely related to but distinct from holomorphic functions. A function of...
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Complex analysis (redirect from Complex function)
concerned with analytic functions of a complex variable, that is, holomorphic functions. The concept can be extended to functions of several complex variables...
18 KB (2,517 words) - 14:08, 22 April 2024
\gamma ^{*}(s,z),} extends the real lower incomplete gamma function as a holomorphic function, both jointly and separately in z and s. It follows from the...
43 KB (7,150 words) - 22:50, 19 August 2024
on this class of functions. In several ways, the harmonic functions are real analogues to holomorphic functions. All harmonic functions are analytic, that...
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Cauchy's integral formula (section Smooth functions)
central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary...
25 KB (4,364 words) - 15:38, 13 August 2024