Calculation of the transformation kernels for the functional transformation method

The main challenge in the application of the Functional Transformation Method is the determination of the transformation kernels for the forward and inverse Sturm-Liouville transformation. This paper presents a straightforward way for their calculation from the eigenfunctions and eigenfrequencies of the underlying physical system. The proposed form of the eigenfunctions is based on a beneficial representation of the matrix exponential. A suitable approach for the calculation of eigenfrequencies is also presented. Two extended examples demonstrate the proposed algorithms.