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

@article{Zudilin2002ATA, title={A Third-Order Ap{\'e}ry-Like Recursion for $\zeta$(5)}, author={V. V. Zudilin}, journal={Mathematical Notes}, year={2002}, volume={72}, pages={733-737} }

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… Expand

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