Abstract
The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the properties of general -conformal mappings and the properties of the mappings, which are hyperbolic analogues of complex elementary functions. We discuss the utility of -conformal mappings to solving 2-dimensional hyperbolic problems of Mathematical Physics.
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