Difference between revisions of "Apéry's constant"
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Latest revision as of 17:17, 24 June 2016
Apéry's constant is the number $\zeta(3)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{k^3}$, where $\zeta$ denotes the Riemann zeta function. This constant is notable because it is known in general that for integers $n$, $\zeta(2n)$ is a rational multiple of $\pi$ but no "nice" closed formula exists for values $\zeta(2n+1)$. Hence it became a notorious open problem to find $\zeta$ at odd integers.
Properties
Apéry's constant is irrational
Relationship between integral of x*log(sin(x)), and Apéry's constant, pi, and logarithm
