Abstract
We consider linear homogeneous difference equations with rational-function coefficients. The search for solutions in the form of the m-interlacing (\(1\leq m\leq {\mathop{\rm ord}} L\), 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.
Supported by ECONET grant 21315ZF.
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Abramov, S.A., Barkatou, M.A., Khmelnov, D.E. (2009). On m-Interlacing Solutions of Linear Difference Equations. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_1
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DOI: https://doi.org/10.1007/978-3-642-04103-7_1
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