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Closed form expressions for two harmonic continued fractions

Published online by Cambridge University Press:  16 October 2017

Martin Bunder  and
Joseph Tonien
Martin Bunder
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Australia e-mail: mbunder@uow.edu.au
Joseph Tonien
Affiliation:
Institute of Cybersecurity and Cryptology, School of Computing and Information Technology, University of Wollongong, Australia e-mail: joseph_tonien@uow.edu.au
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Extract

A continued fraction is an expression of the form

The expression can continue for ever, in which case it is called an infinite continued fraction, or it can stop after some term, when we call it a finite continued fraction. For irrational numbers, a continued fraction expansion often reveals beautiful number patterns which remain obscured in their decimal expansion. The interested reader is referred to [1] for a collection of many interesting continued fractions for famous mathematical constants.

Type
Articles
Information
The Mathematical Gazette , Volume 101 , Issue 552 , November 2017 , pp. 439 - 448
Copyright
Copyright © Mathematical Association 2017 

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References

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