On the Representation of Bicomplex Pseudoanalytic Functions by Integro-differential Operators

We consider a class of bicomplex pseudoanalytic functions which can be characterized by the generalized Bers-Vekua equation Dw = cw* with c = gamma(-1) (D gamma) where D represents the generalized Cauchy-Riemann operator of bicomplex analysis and gamma a suitable solution of the differential equation DD*U - (n(n + 1)/(z + z *)(2))U = 0, n is an element of N. Using a particular Backlund transformation we succeed finding explicit representations for the solutions w by means of certain integro-differential operators. These operators act on bicomplex holomorphic functions. Some cases where the function gamma is of particular form are investigated in detail.