Studies into a matrix technique for calculating prolate spheroidal functions of zero order

A matrix technique for calculating prolate spheroidal functions of zero order that is implemented using the Matlab tools is studied. The calculational accuracy is assessed on the basis of fulfillment of the major properties of the prolate spheroidal functions: invariance to the integral transform with sinc-kernel and to the Fourier transform. An algorithm for properly ordering the functions using their eigenvalues is proposed. Applicability limits of the proposed technique implementation are determined.