Infinite series identities involving quadratic and cubic harmonic numbers. (English) Zbl 1411.11077
Summary: By means of the modified Abel lemma on summation by parts, we investigate infinite series involving quadratic and cubic harmonic numbers. Several infinite series identities are established for \(\pi^2\) and \(\zeta(3)\) as consequences.
MSC:
| 11M06 | \(\zeta (s)\) and \(L(s, \chi)\) |
| 40A25 | Approximation to limiting values (summation of series, etc.) |
