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The Ramanujan Journal

, Volume 38, Issue 2, pp 435–454 | Cite as

Continued reciprocal roots

  • Dixon J. JonesEmail author
Article

Abstract

For \(p\) a real number, a continued \(p\)th power is an expression of the form \(\lim _{n\rightarrow \infty } a_0+(a_1+(a_2+(\ldots +(a_n)^p\ldots )^p)^p)^p.\) Continued reciprocal roots are the special case in which \(-1<p<0\). Following a brief historical survey, we derive a sharp necessary and sufficient divergence condition for continued reciprocal \(q\)th roots of positive terms, where \(q=|1/p|\).

Keywords

Continued power Continued reciprocal root Continued radical Continued root Continued fraction 

Mathematics Subject Classification

40A99 40A05 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Elmer E. Rasmuson LibraryUniversity of Alaska FairbanksFairbanksUSA

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