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Functions of Exponential Type are Differences of Functions of Bounded Index

Published online by Cambridge University Press:  20 November 2018

Shantilal N. Shah
Shantilal N. Shah*
Affiliation:
Department of Mathematics Hampton Institute, Hampton Va. 23668
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The notion of entire function of Bounded Index is by now well established. It may be stated as follows.

An entire function f(z) is said to be of Bounded Index if for some fixed s

for all n and all z. (See [1], [2].)

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 4 , 01 December 1977 , pp. 479 - 483
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Fricke, G. H. Functions of Bounded Index and Their Logarithmic Derivatives, Math. Ann. 206, 215-223.(1973).Google Scholar
2. Hayman, W. K. Differential Inequalities and Local Valency, Pac. Jour, of Math. Vol. 44, No. 1 (1973).Google Scholar
3. Pugh, W. Sum of Functions of Bounded Index. Proc. Amer. Math. Soc. 22, No. 2 (1969).Google Scholar
4. Shah, S. M. Entire Functions of Bounded Index. Proc. Amer. Math. Soc. 19, 1017-1022.(1968).Google Scholar
5. Shah, S. M. and Shah, S. N. A New Class of Functions of Bounded Index, Trans. Amer. Math. Soc, Vol. 173, November 1972, 363-377.Google Scholar