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On orders and types of an entire function over 𝒞k

Published online by Cambridge University Press:  09 April 2009

J. Gopala Krishna
Affiliation:
Department of MathematicsUniversity of Illinois Urbana, Illinois, U. S. A.
I. H. Nagaraja Rao
Affiliation:
Department of MathematicsAndhra University Waltair, A. P., India
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The concepts of order and type associated with an entire function over the complex plane admit different “natural” extensions, most of which are in vogue, for the case of an entire function over 𝒞k, the cartesian product of k copies of the complex plane. This work is concerned with the relations among such extended concepts and with the analogous properties of the concepts.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Bose, S. K. and Sharma, D., ‘Integral functions of two complex variables’, Compositio Mathematica, 15 (1963), 210226.Google Scholar
[2]Fuks, B. A., Introduction to the theory of analytic functions of several complex variables (Amer. Math. Soc., (1963)).CrossRefGoogle Scholar
[3]Krishna, J. Gopala, ‘Maximum term of a power series in one and several complex variables’, Pacific Jour. Math. 29 (1969), 609622.CrossRefGoogle Scholar
[4]Krishna, J. Gopala, ‘Probabilistic techniques leading to a Valinon-type theorem in several complex variables’, Ann. Math. Stat., 41 (1970), 21262129.CrossRefGoogle Scholar
[5]Gross, Fred, ‘Generalized Taylor series and orders and types of entire functions of several complex variables’, Trans. Amer. Math. Soc. 120 (1965), 124144.CrossRefGoogle Scholar