Meromorphic solutions of linear difference equations with polynomial coefficients
2017
scientific article
english
- growth
- difference equation
- Borel exceptional value
EN We study the growth of the transcendental meromorphic solution f(z) of the linear difference equation: ∑j=on pj (z)f (z+j)=q(z), 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.
159 - 168
CC BY-NC-ND (attribution - noncommercial - no derivatives)
public
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