| Version 2 |
Version 1 |
| The harmonic number of order $\theta$ of $n$ is defined as |
The harmonic number of order $\theta$ of $n$ is defined as |
| $$ H_{\theta}(n) = \sum_{i=1}^n \frac{1}{i^{\theta}} $$ |
$$ H_{\theta}(n) = \sum_{i=1}^n \frac{1}{i^{\theta}} $$ |
| Note that $n$ may be equal to $\infty$, provided $\theta > 1$. |
Note that $n$ may be equal to $\infty$, provided $\theta > 1$. |
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If $\theta \le 1$, while $n=\infty$, the harmonic series does not converge and hence the harmonic number does not exist.
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If $\theta \le 1$, $, the harmonic series does not converge and hence the harmonic number does not exist.
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