Meromorphic solutions of a complex difference equation of Malmquist type
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In this paper, we investigate the finite order transcendental meromorphic solutions of complex difference equation of Malmquist type n ∏ i=1 f(z + ci) = R(z, f), where c1, . . ., cn ∈ C＼ {0}, and R(z, f) is an irreducible rational function in f(z) with meromorphic coefficients. We obtain some results on defi- ciencies of the solutions. Using these results, we prove that the growth order of the finite order solution f(z) is 1, if f(z) has Borel exceptional values a(∈ C) and 1. Moreover, we give the forms of f(z).
Abstract
In this paper, we investigate the finite order transcendental meromorphic solutions of complex difference equation of Malmquist type n ∏ i=1 f(z + ci) = R(z, f), where c1, . . ., cn ∈ C＼ {0}, and R(z, f) is an irreducible rational function in f(z) with meromorphic coefficients. We obtain some results on defi- ciencies of the solutions. Using these results, we prove that the growth order of the finite order solution f(z) is 1, if f(z) has Borel exceptional values a(∈ C) and 1. Moreover, we give the forms of f(z).
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