Skip to main content
SpringerLink
Log in

Hypertranscendency of meromorphic solutions of a linear functional equations

  • Published:
aequationes mathematicae Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

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

    K. Ishizaki

Authors
  1. K. Ishizaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: January 19, 1998; revised version: June 25, 1998

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ishizaki, K. Hypertranscendency of meromorphic solutions of a linear functional equations. Aequ. math. 56, 271–283 (1998). https://doi.org/10.1007/s000100050062

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s000100050062

Search

Navigation