Eight infinite series involving harmonic-like numbers are coherently and systematically reviewed. They are evaluated in closed form exclusively by integration together with calculus and complex analysis. In particular, a mysterious series W is introduced and shown to be expressible in terms of the trilogarithm function. Several remarkable integral values and difficult infinite series identities are shown as consequences.
No takes yet. Share an insight, caveat, or question.
Li et al. (2024) studied this question.
Synapse has enriched 4 closely related papers on similar clinical questions. Consider them for comparative context: