Abstract
A linear difference operator L with polynomial coefficients and a function F(x) satisfying the equation LF(x) e 0 are considered. The function is assumed to be analytic in the interval (–σ, d), where σ > 0. In the paper, an implementation of an algorithm suggested by S.A. Abramov and M. van Hoeij for finding conditions that guarantee analyticity of F(x) on the entire real axis \mathbb{R} is presented. The analyticity conditions are linear relations for values of F(x) and its derivatives at a given point belonging to the half-interval l0, d). A procedure for computing values of F(x) and its derivatives up to a prescribed order at a given point x0 e \mathbb{R} is also implemented. Examples illustrating the program operation are presented.
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