A Note on the Integral Representation of Some Relative Growth Indicators of Entire Algebroidal Functions

Year 2018, Issue: 24, 1 - 19, 14.08.2018

Sanjib Kumar Datta Aditi Biswas

Abstract

Let p and q be any two positive integers. In this paper the concept of two
relative growth indicators namely relative (p, q)-th type and relative (p, q)-th weak type of entire
functions with respect to entire algebroidal functions have been introduced from the view point
of their integral representations. Here we also investigate the equivalence of the computational
definitions with their respective integral representations.

Keywords

Entire function, entire algebroidal function, growth, order (lower order), relative order (relative lower order), growth indicator

References

• [1] L. Bernal, Crecimiento relativo de funciones enteras. Contribuci´on al estudio de lasfunciones enteras con ´ındice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.
• [2] L. Bernal, Orden relative de crecimiento de funciones enteras , Collect. Math., 39 (1988), 209-229.
• [3] J. Clunie, The composition of entire and meromorphic functions, Mathematical essays dedicated to A.J.Macintyre, Ohio University Press, (1970), 75 - 92.
• [4] A. S. B. Holland, Introduction to the theory of entire functions, Academic Press, New York and London (1973).
• [5] O. P. Juneja, G. P. Kapoor and 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
• [6] O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the (p, q)-type and lower (p, q)-type of an entire function, J. Reine Agew. Math., 290 (1977), 180-189.
• [7] C. Roy, Some properties of entire functions in one and several complex vaiables, Ph.D. Thesis ( 2010), University of Calcutta.
• [8] L. M. S. Ruiz, S. K. Datta, T. Biswas and G. K. Mondal, On the (p,q)-th relative order oriented growth properties of entire functions,Abstract and Applied Analysis,Hindawi Publishing Corporation, Volume 2014, Article ID 826137, 8 pages.
• [9] E. C. Titchmarsh, The theory of functions, 2nd ed. Oxford University Press, Oxford, 1939.
• [10] G. Valiron, Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.