The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

GROWTH ANALYSIS OF COMPOSITION OF INTEGER TRANSLATED ENTIRE AND MEROMORPHIC FUNCTIONS

  • Received : 2022.09.11
  • Accepted : 2023.05.07
  • Published : 2023.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we study the effect of integer translation on Nevanlinna's characteristic function of a meromorphic function. Also, we investigate comparative growth of integer translated entire and meromorphic functions under different conditions.

Keywords

Acknowledgement

The authors are grateful to the referees and the editor for their corrections and suggestions, which have greatly improved the readability of the paper.

References

  1. E. Borel: Sur les z'eros des fonctions enti'eres. Acta Math. 20 (1897), 357-396. DOI: 10.1007/BF02418037
  2. W. Bergweiler: On the Nevanlinna characteristic of a composite function. Complex Variables 10 (1988), 225-236. https://doi.org/10.1080/17476938808814301
  3. T. Biswas & S.K. Datta: Effect of integer translation on relative order and relative type of entire and meromorphic functions. Commun. Korean Math. Soc. 33 (2018), no. 2, 485-494. https://doi.org/10.4134/CKMS.c170162
  4. S.K. Datta & S. Tamang: Some growth properties on integer translation of entire and meromorphic functions. International journal of advanced scientific and technical research 06 (2012), no. 2, 485-492. https://rspublication.com/ijst/dec12/45.pdf
  5. S.K. Datta, T. Biswas & M. Biswas: Few relations on the growth rates of composite entire functions using their (p, q) th order. Tamkang Journal of Mathematics 44 (2013), no. 3, 289-301. doi:10.5556/j.tkjm.44.2013.1198
  6. W.K. Hayman: Meromorphic Functions. The Clarendon Press, Oxford, 1964. ISBN o I8535Io 4
  7. O.P. Juneja, G.P. Kapoor & S.K. Bajpai: On the (p, q)-order and lower (p, q)-order of an entire function. J. Reine Angew. Math. 282 (1976), 53-67. http://eudml.org/doc/151700
  8. Q. Lin & C. Dai: On a conjecture of Shah concerning small functions. Kexue Tong bao (English Ed.) 31 (1986), no. 4, 220-224.
  9. R. Nevanlinna: Zur theorie der merophen funktionen. Acta Math. 45 (1925), 1-99. DOI:10.1007/bf02543858
  10. D. Sato: On the rate of growth of entire functions of fast growth. Bull. amer. math. soc. 69 (1963), no. 3, 411-414. DOI:https://doi.org/10.1090/S0002-9904-1963-10951-9
  11. S. Tamang & N. Biswas: Some results on the integer translation of composite entire and meromorphic functions. Kanuralp Journal of Mathematics 5 (2017), no. 2, 1-11. https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/28490/342088
  12. G. Valiron: Lectures on the General Theory of Integral Functions. Chelsea Publishing Company, 1949. ISBN/ASIN 1406728985