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arXiv · 1606.07109

Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation

Carlos E. Arreche
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Abstract

We apply the difference-differential Galois theory developed by Hardouin and Singer to compute the differential-algebraic relations among the solutions to a second-order homogeneous linear difference equation of the form $ y(x+2)+a(x)y(x+1)+b(x)y(x)=0,$ where the coefficients $a(x),b(x)\in \bar{\mathbb{Q}}(x)$ are rational functions in $x$ with coefficients in $\bar{\mathbb{Q}}$. We develop algorithms to compute the difference-differential Galois group associated to such an equation, and show how to deduce the differential-algebraic relations among the solutions from the defining equations of the Galois group.

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Carlos E. Arreche. 2016-06-22. Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation. https://doi.org/10.1142/s0219199716500565

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