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AN EXACT FORMULA FOR THE HARMONIC CONTINUED FRACTION
Published online by Cambridge University Press: 10 June 2020
Abstract
For a positive real number $t$, define the harmonic continued fraction
$$\begin{eqnarray}\text{HCF}(t)=\biggl[\frac{t}{1},\frac{t}{2},\frac{t}{3},\ldots \biggr].\end{eqnarray}$$
$$\begin{eqnarray}\text{HCF}(t)=\frac{1}{1-2t(\frac{1}{t+2}-\frac{1}{t+4}+\frac{1}{t+6}-\cdots \,)}.\end{eqnarray}$$
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 11 - 21
- Copyright
- © 2020 Australian Mathematical Publishing Association Inc.