Infinite product for e^{6ζ(3)}



Abstract

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.


Keywords

summation methods; infinite series; infinite products

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Published : 2007-09-28


GenčevM. (2007). Infinite product for e^{6ζ(3)}. Annales Mathematicae Silesianae, 21, 41-48. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14061

Marian Genčev  marian.gencev@osu.cz
Department of Mathematics, University of Ostrava, Czech Republic  Czechia



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