Annales Academić Scientiarum Fennicć
Mathematica
Volumen 38, 2013, 855-871

THE RECIPROCAL OF A REAL ENTIRE FUNCTION AND NON-REAL ZEROS OF HIGHER DERIVATIVES

James K. Langley

University of Nottingham, School of Mathematical Sciences
Nottingham, NG7 2RD, United Kingdom; jkl@maths.nott.ac.uk

Abstract. Two theorems are proved concerning non-real zeros of derivatives of the reciprocal of a real entire function with real zeros. A further result treats the frequency of non-real poles for real meromorphic functions which together with their first three derivatives have only real zeros.

2010 Mathematics Subject Classification: Primary 30D20, 30D35.

Key words: Meromorphic function, non-real zeros.

Reference to this article: J.K. Langley: The reciprocal of a real entire function and non-real zeros of higher derivatives. Ann. Acad. Sci. Fenn. Math. 38 (2013), 855-871.

Full document as PDF file

doi:10.5186/aasfm.2013.3847