Generalized order of entire monogenic functions of slow growth

Volume 5, Issue 6, pp 418--425 http://dx.doi.org/10.22436/jnsa.005.06.02

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Authors

Susheel Kumar - Department of Mathematics, Central University of Himachal Pradesh, Dharamshala-176215, India. Kirandeep Bala - Department of Mathematics, Central University of Himachal Pradesh, Dharamshala-176215, India.

Abstract

In the present paper we study the generalized growth of entire monogenic functions having slow growth. The characterizations of generalized order of entire monogenic functions have been obtained in terms of their Taylor's series coefficients.

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Keywords

• Clifford algebra
• Clifford analysis
• Generalized Cauchy-Riemann system
• Entire monogenic function
• Generalized order.

MSC

•  30G35
•  30D15

References

• [1] D. Constales, R. De Almeida, R. S. Krausshar, On the growth type of entire monogenic functions, Arch. Math. , 88 (2007), 153-163.


• [2] D. Constales, R. De Almeida, R. S. Krausshar, On the relation between the growth and the Taylor coefficients of entire solutions to the higher dimensional Cauchy-Riemann system in \(\mathbb{R}^{n+1}\), J. Math. Anal. App. , 327 (2007), 763-775.


• [3] G. P. Kapoor, A. Nautiyal, Polynomial approximation of an entire function of slow growth, J. Approx. Theory, 32 (1981), 64-75.


• [4] M. N. Seremeta, On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion , Amer. Math. Soc. Trans., 88 (1970), 291-301.