Euler's Integral Theorem

Theorem

 * $H_n = \ln n + \gamma + \map \OO {\dfrac 1 n}$

where:
 * $H_n$ denotes the $n$th harmonic number
 * $\gamma$ denotes the Euler-Mascheroni constant
 * $\map \OO {\dfrac 1 n}$ denotes big-$\OO$ of $\dfrac 1 n$.