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An improved Cauchy formula for hypermonogenic functions. (English) Zbl 1172.30027

Summary: A new Cauchy-type formula for hypermonogenic functions is derived. Hypermonogenic functions, introduced in [S.-L. Eriksson-Bique and H. Leutwiler, Ryan, John (ed.) et al., Clifford algebras and their applications in mathematical physics. Papers of the 5th international conference, Ixtapa-Zihuatanejo, Mexico, June 27–July 4, 1999. Volume 2: Clifford analysis. Boston, MA: Birkhäuser. Prog. Phys. 19, 287–302 (2000; Zbl 0965.30020)], are a generalization of holomorphic functions to several dimensions. The power function \(x^{m}\) is hypermonogenic.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
30A05 Monogenic and polygenic functions of one complex variable

Citations:

Zbl 0965.30020
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