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ANALYTIC FUNCTIONS AND μ-REGULAR FUNCTIONS: A COMPARATIVE STUDY
Keywords:
μ-regular, analytic function, Cauchy-Riemann equationDOI:
https://doi.org/10.17654/0972087126005Abstract
This article examines the basic concept of a μ-regular function compared to an analytic function, in connection with the fact that these two complex functions are built from panharmonic functions and harmonic functions, which are solutions of the Yukawa equation and the Laplace partial differential equation, respectively. The two differential equations differ only in that the Yukawa equation has a positive constant on the right-hand side, while the Laplace equation has a zero constant there. In general, the Laplace equation is a special case of the Yukawa equation.
Similarly, the complex-valued functions constructed from these two real-valued functions, namely, harmonic and panharmonic functions are considered. Analytic functions are those whose real and imaginary parts are harmonic functions and which satisfy the Cauchy-Riemann equations, whereas μ-regular functions are complex functions whose real and imaginary parts are panharmonic functions and satisfy the generalized Cauchy-Riemann equations. In fact, if in the generalized Cauchy-Riemann equations, then the standard Cauchy-Riemann equations are recovered.
Received: May 2, 2025
Revised: July 12, 2025
Accepted: July 28, 2025
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