Solution of the difference equation for Gauss' hypergeometric function by use of the tau method

Abstract

AbstractIn two previous papers the idea of the tau method to get approximate solutions of differential equations was extended to get like results for difference equations. The models treated were the difference equation for the reciprocal of the gamma function and the difference equation for the entire part of the Bessel function of the first kind. In this paper, we apply the tau method as described in the title of this paper. Some numerics are presented which indicate that the process is convergent.In this connection an ‘a posteriori’ error analysis for the Bessel function case is presented. How this analysis could be extended to the model of the present paper is discussed, but further analysis is deferred to future research