An Apery-like Difference Equation for Catalan's Constant

@article{Zudilin2003AnAD,
  title={An Apery-like Difference Equation for Catalan's Constant},
  author={W. Zudilin},
  journal={Electron. J. Comb.},
  year={2003},
  volume={10}
}
  • W. Zudilin
  • Published 2003
  • Mathematics, Computer Science
  • Electron. J. Comb.
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, we obtain a second-order dierence equation for these forms and their coecients. As a consequence we derive a new way of fast calculation of Catalan’s constant as well as a new continued-fraction expansion for it. Similar arguments are put forward to deduce a second-order dierence equation and a new continued… Expand

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