A Third-Order Apéry-Like Recursion for ζ(5)

@article{Zudilin2002ATA,
  title={A Third-Order Ap{\'e}ry-Like Recursion for ζ(5)},
  author={V. V. Zudilin},
  journal={Mathematical Notes},
  year={2002},
  volume={72},
  pages={733-737}
}
  • V. V. Zudilin
  • Published 2002
  • Mathematics
  • Mathematical Notes
  • In 1978, Apery has given sequences of rational approximations to $\zeta(2)$ and $\zeta(3)$ yielding the irrationality of each of these numbers. One of the key ingredient of Apery's proof are second-order difference equations with polynomial coefficients satisfied by numerators and denominators of the above approximations. Recently, a similar second-order difference equation for $\zeta(4)$ has been discovered. The note contains a possible generalization of the above results for the number $\zeta… CONTINUE READING

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