Corpus ID: 87012

A FEW REMARKS ON LINEAR FORMS INVOLVING CATALAN'S CONSTANT

@article{Zudilin2002AFR,
  title={A FEW REMARKS ON LINEAR FORMS INVOLVING CATALAN'S CONSTANT},
  author={W. Zudilin},
  journal={arXiv: Number Theory},
  year={2002}
}
  • W. Zudilin
  • Published 2002
  • Mathematics
  • arXiv: Number Theory
In the joint work (RZ) of T. Rivoal and the author, a hypergeometric construction was proposed for studing arithmetic properties of the values of Dirichlet's beta function �(s) at even positive integers. The construction gives some bonuses (RZ), Section 9, for Catalan's constant G = �(2), such as a second-order Apery-like recursion and a permutation group in the sense of G. Rhin and C. Viola (RV). Here we prove expected integrality properties of solutions to the above recursion as well as… Expand
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  • W. Zudilin
  • Mathematics, Computer Science
  • Electron. J. Comb.
  • 2003
TLDR
Applying Zeilberger's algorithm of creative telescoping to a family of certain very-well-poised hypergeometric series involving linear forms in Catalan’s constant with rational coecients, a second-order dierence equation is obtained and a new way of fast calculation of Catalan's constant as well as a new continued-fraction expansion for it is derived. Expand
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An Apery-like Difference Equation for Catalan's Constant
  • W. Zudilin
  • Mathematics, Computer Science
  • Electron. J. Comb.
  • 2003
TLDR
Applying Zeilberger's algorithm of creative telescoping to a family of certain very-well-poised hypergeometric series involving linear forms in Catalan’s constant with rational coecients, a second-order dierence equation is obtained and a new way of fast calculation of Catalan's constant as well as a new continued-fraction expansion for it is derived. Expand
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