On m-Interlacing Solutions of Linear Difference Equations
نویسندگان
چکیده
We consider linear homogeneous difference equations with rational-function coefficients. The search for solutions in the form of the minterlacing (1 ≤ m ≤ ord L, where L is a given operator) of finite sums of hypergeometric sequences, plays an important role in the Hendriks–Singer algorithm for constructing all Liouvillian solutions of L(y) = 0. We show that Hendriks–Singer’s procedure for finding solutions in the form of such m-interlacing can be simplified. We also show that the space of solutions of L(y) = 0 spanned by the solutions of the form of the m-interlacing of hypergeometric sequences possesses a cyclic permutation property. In addition, we describe adjustments of our implementation of the Hendriks–Singer algorithm to utilize the presented results.
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