On boundary values for rectifiable curves of a generalization of the Cauchy-type integral related to the Helmholtz operator in R²

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There are considered vector fields and quaternionic α-hyperholomorphic functions in a domain of R² which generalize the notion of solenoidal and irrotational vector fields. There are established sufficient conditions for the corresponding Cauchy-type integral along a closed Jordan rectifiable curve to be continuously extended onto the closure of a domain. The Sokhotski-Plemelj-type formulas are proved as well.