A proof that Euler missed ...

@article{Poorten1979APT,
  title={A proof that Euler missed ...},
  author={Alfred J. van der Poorten and R. Ap{\'e}ry},
  journal={The Mathematical Intelligencer},
  year={1979},
  volume={1},
  pages={195-203}
}
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176 Citations

176 Citations

Citation Type

Citation Type

Further Apéry-Like Series for Riemann Zeta Function
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Abstract By means of two transformation formulas of classical hypergeometric series, several Apéry-like series involving harmonic numbers of higher order are derived for the Riemann zeta function,…
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Infinite series identities derived from the very well-poised $$\Omega $$ Ω -sum
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Recurrence equation and integral representation of Apéry sums
  • M. Uhl
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    European Journal of Mathematics
  • 2020
Various methods are used to investigate sums involving a reciprocal central binomial coefficient and a power term. In the first part, new functions are introduced for calculation of sums with a…
On two congruences involving Franel numbers
  • Ji-Cai Liu
  • Mathematics
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
  • 2020
Via symbolic summation method, we establish the following series for $\pi^2$: \begin{align*} \sum_{k=1}^\infty \frac{H_k-2H_{2k}}{(-3)^k k} = \frac{\pi^2}{18}, \end{align*} where $H_k=\sum_{j=1}^k…
A note on the number of irrational odd zeta values
Abstract We prove that, for any small $\varepsilon > 0$, the number of irrationals among the following odd zeta values: $\zeta (3),\zeta (5),\zeta (7),\ldots ,\zeta (s)$ is at least $( c_0 -…
Hypergeometric rational approximations to ζ(4)
Abstract We give a new hypergeometric construction of rational approximations to ζ(4), which absorbs the earlier one from 2003 based on Bailey's 9F8 hypergeometric integrals. With the novel…
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