Representation of Quaternionic $ψ$-hyperholomorphic Functions
In the algebra of complex quaternions $\mathbb{H(C)}$ we consider for the first time left- and right-$ψ$-hyperholomorphic functions. We justify the transition in left- and right-$ψ$-hyperholomorphic functions to a simpler basis i.e. to the Cartan basis. Using Cartan's basis we find the solution of Cauchy-Fueter equation. By the same method we find a representation of left-$ψ$-hyperholomorphic function in a special case.
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