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The hyperexponential function an exercise in convergence

Published online by Cambridge University Press:  01 August 2016

Arthur Ellis-Davies
Arthur Ellis-Davies*
Affiliation:
Swn Y Mor, Aberdesach, Caernarfon, Gwynedd LL54 5EW email: a.ellisdavies@btinternet.com
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Extract

For positive x, define the sequence of functions {hn(x)} thus:

So, for example,

x appearing 3 times,

and x appearing 5 times.

The hyperexponential function is then defined as

for those values of x for which this limit exists. Since an infinite number of operations are involved, we clearly need to study carefully the question of convergence.

Information

Type
Articles
Information
The Mathematical Gazette , Volume 93 , Issue 527 , July 2009 , pp. 193 - 199
Copyright
Copyright © The Mathematical Association 2009

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References

1. Spivak, M., Calculus (3rd edn.), Cambridge University Press.Google Scholar