Definition D1 The nnnth harmonic number is defined as Hn=1+12+13+⋯+1n=∑k=1n1k ,n≥0.H_n = 1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n} = \sum_{k=1}^n \frac{1}{k} \;, \quad n \geq 0. Hn=1+21+31+⋯+n1=k=1∑nk1,n≥0.