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On entire functions with gap power series

Published online by Cambridge University Press:  18 May 2009

J. M. Anderson  and
K. G. Binmore
J. M. Anderson
Affiliation:
University College, London
K. G. Binmore
Affiliation:
London School of Economics
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In this note we consider transcendental entire functions

whose power series contain gaps, i.e.

where Λ = {λk} is a suitable set of positive integers. We denote the set of all such functions f(z) by E(Λ). As usual M(r) = M(r, f) denotes the maximummodulus of f(z) on the circle |z| = r. The order p and the lower order λ of f(z) are defined by

respectively.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 12 , Issue 2 , September 1971 , pp. 89 - 97
Copyright
Copyright © Glasgow Mathematical Journal Trust 1971

References

REFERENCES

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