Computational Methods and Function Theory

, Volume 1, Issue 1, pp 27–39

Complex Difference Equations of Malmquist Type


    • Department of MathematicsUniversity of Joensuu
  • Risto Korhonen
    • Department of MathematicsUniversity of Joensuu
  • Ilpo Laine
    • Department of MathematicsUniversity of Joensuu
  • Jarkko Rieppo
    • Department of MathematicsUniversity of Joensuu
  • Kazuya Tohge
    • Faculty of TechnologyKanazawa University

DOI: 10.1007/BF03320974

Cite this article as:
Heittokangas, J., Korhonen, R., Laine, I. et al. Comput. Methods Funct. Theory (2001) 1: 27. doi:10.1007/BF03320974


In a recent paper [1], Ablowitz, Halburd and Herbst applied Nevanlinna theory to prove some results on complex difference equations reminiscent of the classical Malmquist theorem in complex differential equations. A typical example of their results tells us that if a complex difference equation y(z + 1) + y(z − 1) = R(z, y) with R(z, y) rational in both arguments admits a transcendental meromorphic solution of finite order, then degyR(z, y) ≤ 2. Improvements and extensions of such results are presented in this paper. In addition to order considerations, a result (see Theorem 13) is proved to indicate that solutions having Borel exceptional zeros and poles seem to appear in special situations only.


Complex difference equationvalue distributionNevanlinna characteristicBorel exceptional values

2000 MSC


Copyright information

© Heldermann Verlag 2001