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.
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Vol. 21 (2007)
Published: 2007-09-28
10.1515/amsil
English