Symbolic Computation Applied to Cauchy Type Singular Integrals

The development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At present time, this has wide applications study non-linear differential equations, linear transport theory, diffraction acoustic electromagnetic waves, scattering inverse scattering, among others. In our work, we use computer algebra system Mathematica implement, for first time on a computer, analytical algorithms developed us others within theory. main goal paper new related Cauchy type singular integrals, defined unit circle. design these was focused possibility implementing all extensive symbolic numeric calculations algorithms. Several nontrivial examples computed with are presented. corresponding source code been made available as supplement online edition article.