Harmonic number

In Mathematical, the harmonic numbers of order $n\; \backslash ,$ is given by

$H^\; \{(m)\}\_n=\; \backslash \; sum\_\; \{k=1\}\; ^n\; \backslash \; frac\; \{1\}\; \{k^m\}\; \backslash ,$.

The particular case $m=1\; \backslash ,$ is frequently written without the exhibitor, in the form

$H\_n=\; \backslash \; sum\_\; \{k=1\}\; ^n\; \backslash \; frac\; \{1\}\; \{K\}\; \backslash ,$.

In extreme cases $n\; \backslash \; rightarrow\; \backslash \; infty\; \backslash ,$, the harmonic numbers converge towards the Fonction Zeta of Riemann.

The sum connected $\backslash \; sum\_\; \{k=1\}\; ^n\; k^m\; \backslash ,$ appears in the study of the numbers of Bernoulli.

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