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aequationes mathematicae

, Volume 56, Issue 3, pp 271–283 | Cite as

Hypertranscendency of meromorphic solutions of a linear functional equations

  • K. Ishizaki
Article

Abstract.

In this note we treat the functional equation \(f(cz)=a(z)f(z)+b(z)\), where c is a constant \(|c|\ne1\), 0, and a(z), b(z) are rational functions. It is shown that no transcendental meromorphic solution of the functional equation satisfies an algebraic differential equation with rational coefficients.

Keywords. Meromorphic functions, hypertranscendency. 

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Copyright information

© Birkhäuser Verlag, Basel, 1998

Authors and Affiliations

  • K. Ishizaki
    • 1
  1. 1.Department of Mathematics, NIPPON Institute of Technology, 4‐1 Gakuendai Miyashiro Minamisaitama, Saitama 345‐8501, Japan Japan

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