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Meromorphic solutions of linear difference equations with polynomial coefficients

Zhang Y., Gao Z., Zhang H.

Fasciculi Mathematici

2017

Nr 59

159--168

We study the growth of the transcendental meromorphic solution f(z) of the linear difference equation: [formula] where q(z), p0(z), . . ., pn(z) (n ≥ 1) are polynomials such that p0(z)pn(z) ≠ 0, and obtain some necessary conditions guaranteeing that the order of ƒ(z) satisfies σ(ƒ) ≥ 1 using a difference analogue of the Wiman-Valiron theory. Moreover, we give the form of ƒ(z) with two Borel exceptional values when two of p0(z), . . ., pn(z) have the maximal degrees.