ζ(3) was named Apéry's constant after the French mathematician Roger Apéry, who proved in 1978 that it is an irrational number. [4] This result is known as Apéry's theorem. The original …

从ζ(3)的表达式，再结合T.Rivoal的方法可知，ζ(3)是 无理数 。 可以证明，集合 \small\{\zeta(2n+1)\ |\ n\in\mathbb N\} 内 存在无穷多个无理数元素 。 也可以通过 伯努利多项 …

Apéry's constant is defined by zeta(3)=1.2020569..., (1) (OEIS A002117) where zeta(z) is the Riemann zeta function. Apéry (1979) proved that zeta(3) is irrational, although it is not known if …

In mathematics, Apéry's theorem is a result in number theory that states the Apéry's constant ζ (3) is irrational. That is, the number. cannot be written as a fraction where p and q are integers. …

The question is whether or not $\zeta(3)$ is connected with $\pi$. The answer is yes. Moreover, $\zeta(3) = \beta \pi^{\alpha}$ for some complex $\alpha, \beta$. Take $\alpha = 3$ and $\beta …

Dec 19, 2024 · The value of the zeta function ζ(3) had been an open question for more than 200 years. The brilliant Swiss mathematician Leonhard Euler had cut his teeth on it and failed to …

The value ζ(3) is also known as Apéry's constant and has a role in the electron's gyromagnetic ratio.

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而在本文中，将介绍一个不那么常见的数 \zeta (3) 的无理性的证明。 我们熟知黎曼 \zeta 函数定义为 \zeta (s)=\displaystyle\sum_ {n=1}^\infty\dfrac1 {n^s} ，它被广泛应用于解决一些解析数论 …

Aug 28, 2021 · There are closed-form expressions for ζ (s) when s is an even integer [2] but so far not nobody has found one for s = 3. The value of ζ (3) is sometimes called Apéry’s constant …