AN EXACT FORMULA FOR THE HARMONIC CONTINUED FRACTION
| Autor: | Joseph Tonien, Peter Nickolas, Martin W. Bunder |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Bulletin of the Australian Mathematical Society. 103:11-21 |
| ISSN: | 1755-1633 0004-9727 |
| Popis: | For a positive real number $t$, define the harmonic continued fraction $$\begin{eqnarray}\text{HCF}(t)=\biggl[\frac{t}{1},\frac{t}{2},\frac{t}{3},\ldots \biggr].\end{eqnarray}$$ We prove that $$\begin{eqnarray}\text{HCF}(t)=\frac{1}{1-2t(\frac{1}{t+2}-\frac{1}{t+4}+\frac{1}{t+6}-\cdots \,)}.\end{eqnarray}$$ |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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