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Cauchy integral formula for k-monogenic function with \({\alpha}\)-weight. (English) Zbl 1394.30037
Summary: Firstly, we give the definition of k-monogenic function with \(\alpha \)-weight in Clifford analysis and discuss a series of properties of this function. Then, we get the Cauchy-Pompeiu formula for k-monogenic function with \(\alpha \)-weight. Lastly, we prove the Cauchy integral theorem for k-monogenic function with \(\alpha \)-weight.
MSC:
30G35 Functions of hypercomplex variables and generalized variables
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
30E25 Boundary value problems in the complex plane
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