On the harmonic continued fractions
| Autor: | Joseph Tonien, Peter Nickolas, Martin W. Bunder |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Algebra and Number Theory
010102 general mathematics Harmonic (mathematics) 0102 computer and information sciences 01 natural sciences Convolution Combinatorics symbols.namesake Number theory Integer 010201 computation theory & mathematics Fourier analysis symbols Euler's formula Stirling number Fraction (mathematics) 0101 mathematics Mathematics |
| Zdroj: | The Ramanujan Journal. 49:669-697 |
| ISSN: | 1572-9303 1382-4090 |
| Popis: | In this paper, we study the harmonic continued fractions. These form an infinite family of ordinary continued fractions with coefficients $$\frac{t}{1}, \frac{t}{2}, \frac{t}{3}, \ldots $$ for all $$t>0$$ . We derive explicit formulas for the numerator and the denominator of the convergents. In particular, when t is an even positive integer, we derive the limit value of the harmonic continued fraction. En route, we define and study convolution alternating power sums and prove some identities involving Euler polynomials and Stirling numbers, which are of independent interest. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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