# zbMATH — the first resource for mathematics

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.
Reviewer: Reviewer (Berlin)

##### MSC:
 30G35 Functions of hypercomplex variables and generalized variables 30A05 Monogenic and polygenic functions of one complex variable
##### Keywords:
hypermonogenic function; Dirac operator; hyperbolic metric
Full Text: