Infinite series of convergence rate $-1/8$ suggested by two formulae of Guillera
Volume 132 / 2024
Annales Polonici Mathematici 132 (2024), 153-167
MSC: Primary 11B65; Secondary 11M06, 65B10
DOI: 10.4064/ap230401-17-12
Published online: 29 February 2024
Abstract
By applying the coefficient extraction method to nonterminating hypergeometric sums, we establish fifteen closed formulae for infinite series involving both harmonic numbers and cubic central binomial coefficients, including some formulae conjectured by Z.-W. Sun.
