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We compute the Bergman reproducing kernel for  monogenic functions for half-ball, more general orthogonal ball sectors, and for  fractional wedge domains. In the results we obtain the terms to be expected from  analogy with complex analysis, viz in the first case the Bergman kernels for the  half-space and the entire ball, and in the second the sum of rotated half-space  Bergman kernels, but in both cases there also occur supplementary, purely  hypercomplex correction terms. Finally, applying a periodisation argument we  obtain closed and explicit formulas for the Bergman kernels of wedge shaped  domains that are rectangularly bounded.

The Bergman Kernels for the half-ball and for fractional wedge-shaped domains in Clifford Analysis