Abstract
In this paper we introduce generalized $$(k_i)$$ -monogenic functions in Clifford analysis. They are the general types of the k-hypermonogenic functions founded by Leutwiler and Eriksson. Each component of a generalized $$(k_i)$$ -monogenic function is a solution of a generalized Weinstein’s equation. We will construct $$2^n$$ generalized Cauchy kernels and give an integral representation of the generalized $$(k_i)$$ -monogenic functions.
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