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 …

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 …

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 …

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

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 …

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ , is a mathematical function of a complex variable defined as () = = = + + + for ⁡ >, and its analytic …

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 …

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"A natural question is whether Zeta(3) is a rational multiple of Pi^3. This is not known, though in 1978 R. Apéry succeeded in proving that Zeta(3) is irrational. In Chapter 8 we pointed out that …

I mean "brutal force" by summing handly or in a computer, the original formula for $\zeta(3)$. It is known that the given series converges very slowly. Apéry's rational approximation $a_n/b_n$ …