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http://dx.doi.org/10.4134/BKMS.2014.51.6.1735

MEROMORPHIC SOLUTIONS OF A COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE  

Zhang, Ran-Ran (Department of Mathematics Guangdong University of Education)
Huang, Zhi-Bo (School of Mathematical Sciences South China Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.6, 2014 , pp. 1735-1748 More about this Journal
Abstract
In this paper, we investigate the finite order transcendental meromorphic solutions of complex difference equation of Malmquist type $$\prod_{i=1}^{n}f(z+c_i)=R(z,f)$$, where $c_1,{\ldots},c_n{\in}\mathbb{C}{\backslash}\{0\}$, and R(z, f) is an irreducible rational function in f(z) with meromorphic coefficients. We obtain some results on deficiencies 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 $a({\in}\mathbb{C})$ and ${\infty}$. Moreover, we give the forms of f(z).
Keywords
difference equation; meromorphic function; deficiency;
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