Apéry's Constant in terms of Central Binomial Coefficients

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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


Sources