Description

• Title:
  Infinite product for e^{6ζ(3)}
• Creator:
  Genčev, Marian
• Description:
  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.
• Object availability:
  free access
• Date:
  2007.09.28
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol. 21 (2007); 41-48;
  Annales Mathematicae Silesianae; Tom 21 (2007); 41-48;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/14061/10761
• Subject:
  summation methods;
  infinite series;
  infinite products
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/14061
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  seek permission
• Type:
  other