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

作者：Arreche Carlos E

来源：Communications in Contemporary Mathematics, 2017, 19(6): 1650056.

DOI：10.1142/S0219199716500565

• Difference equations
• differential equations
• difference Galois theory
• difference-differential Galois theory

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 y(x + 2) + a(x) y(x + 1) + b(x) y(x) = 0, where the coefficients a(x), b(x) is an element of (Q) over bar (x) are rational functions in x with coefficients in (Q) over bar. 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.

• 出版日期2017-12