Abstract
The object of this work is to use functions of a generalized complex variable to solve the problems of fluid dynamics and elasticity theory. In this paper, we obtain Cauchy-Riemann conditions, generalized Laplace equation and the generalized Poisson formula for such functions.
Highlights
The generalized complex numbers are divided into types such as elliptic, hyperbolic and parabolic complex numbers [1]
This means the following: let a generalized complex number be in this form z = x + py, p2 = −θ0 + pθ1, where θ0, θ1 are real numbers
0, such generalized complex numbers refer to the elliptic type
Summary
The generalized complex numbers are divided into types such as elliptic, hyperbolic and parabolic complex numbers [1]. This means the following: let a generalized complex number be in this form z = x + py, p2 = −θ0 + pθ, where θ0, θ1 are real numbers. If it is set that θ0 = 1, θ1 = 0, we obtain usual complex numbers. We consider the theory of analytical functions f z = u x, y + pv x, y of the generalized complex variable z = x + py, satisfying a set of Cauchy-Riemann equations ux + θ1vx = vy, uy + θ0vx = 0,.
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