Hyperharmonic series involving Hurwitz zeta function
For integers \(r\geq 1\) and \(m\geq r+1\) the authors prove that \[ \sum_{n=1}^\infty\frac{H_n^{(r)}}{n^m}=\sum_{n=1}^\infty H_n^{(r-1)}\sum_{p=0}^\infty\frac{1}{(n+p)^m}, \] where \(H_n^{(r)}\) are the hyperharmonic numbers.
scientific article; zbMATH DE number 5655000