In the first part of this paper, resorting to the idea of Hadamard principle value and induction,we discuss the inductive definition, existence of Hadamard principle value, recursive formula, computation formula, differential formula on the sense of Hadamard principle value for several kinds of quasi-Bochner-Martinelli-type high order singular integrals with one singular point. Then, in the second part,the above properties of quasi-Bochner-Martinelli-type high order singular integrals with two singular points are discussed.
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