Apéry's Constant in terms of Central Binomial Coefficients

Theorem

Apéry's constant can be expressed in terms of binomial coefficients as:

$\map \zeta 3 = \ds \dfrac 5 2 \sum_{n \mathop = 1}^\infty \dfrac {\paren {-1}^{n - 1} } {n^3 \dbinom {2 n} n}$


Proof


This theorem requires a proof.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
To discuss this page in more detail, feel free to use the talk page.
When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.


Sources

  • 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,20205 69 \ldots$
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.