The global Borel-Pompeiu-type formula for generalized partial-slice monogenic functions

The global Borel-Pompeiu-type and Cauchy-type integral formulas are proposed by examining the connection between the space of generalized partial-slice regular functions and a non-constant coefficient differential operator specified by G=‖x→‖2∑k=1p∂xk+x→∑k=p+1p+qxk∂xk. Structural sets, ψ-differential operators, and reproducing functions like Aψ and Bψ to formulate formulas are introduced. These formulas generalize existing results for quaternionic and Clifford slice monogenic functions, enabling new proofs of properties of generalized partial-slice monogenic functions, thus enriching Clifford analysis theory with potential applications in geometry, physics, and engineering.