Infinite product for e^6ζ(3) - Genčev, Marian (Annales Mathematicae Silesianae, 2007)
The author uses the summation of rational series using the properties of the digamma function Ψ(x) and the methods of the residue calculus to evaluate the function Hα(x) for α = 1 and x = a−1(N), N∈ℕ (see Theorem 1) which is called the function generating the generalized harmonic numbers of order 1 (see Definition 1). The relation between the functions H1(x), x > 0, and Ψ(x) is used to find the approximations of the constant e6ζ(3) in the form of the infinite product which contains only the numbers e, π and the roots of unity, where ζ(3) is the Apéry constant.