MEROMORPHIC SOLUTIONS OF q-DIFFERENCE EQUATIONS

Abstract

Consider a linear q-difference equation: a(z)f(z) = b(z)f(qz) + c(z), 0 < |q| < 1, a(z), b(z), c(z) ∈ C[z]. We suppose that it admits a transcendental meromorphic solution f (z). Here we will determine the counting function N(r, f), and investigate the deficiency property of f (z). Finally, we give some examples.