  The construction of a pair of transmutation operators for the radial main
Vekua equation with a Bicomplex-valued coefficient is presented. The pair of
operators transform the Bicomplex analytic functions into the solutions of the
main Vekua equation. The analytical properties of the operators in the space of
classical solutions and the pseudoanalytic Bergman space are established. With
the aid of such operators, a complete system of solutions for the main Vekua
equation, called radial formal powers, is obtained. The completeness of the
radial formal powers is proven with respect to the uniform convergence on
compact subsets and in the Bicomplex pseudoanalytic Bergman space with the
$L_2$-norm. For the pseudoanalytic Bergman space on a disk, we show that the
radial formal powers are an orthogonal basis, and a representation for the
Bergman kernel in terms of such basis is obtained.

Complex Variables;Analysis of PDEs;Classical Analysis and ODEs