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Iterating exponential functions with cyclic exponents

Published online by Cambridge University Press:  24 October 2008

I. N. Baker  and
P. J. Rippon
I. N. Baker
Affiliation:
Department of Mathematics, Imperial College, London SW7 2BZ
P. J. Rippon
Affiliation:
Faculty of Mathematics, Open University, Milton Keynes MK7 6AA
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Extract

This paper is concerned with expressions of the form

where fa(x) = ax. Thus we have

Such expressions have been described variously as continued exponentials, iterated exponentials, towers of exponents or hyperpowers. We shall frequently make use of their elementary properties, as for example

and

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 357 - 375
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

REFERENCES

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