In mathematics, the Riemann zeta function is a function in complex analysis, which is also important in number theory. It is often denoted and is named after the mathematician Bernhard …

Are there any nice ways to prove that $$\zeta(4) = \sum_{n=1}^{\infty} \frac{1}{n^4} = \frac{\pi^4}{90}?$$ I already know some proofs that give all values of $\zeta(n)$ for positive …

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2025年2月9日 · The Riemann Zeta Function of 4 was solved by Leonhard Euler, using the same technique as for the Basel Problem. If only my brother were alive now. -- Johann Bernoulli

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 …

2022年11月8日 · We derive a more longer yet beautiful proof of the value of ζ (4) using the multiplication table of the (ζ (2))^2 and utilziing some double sum properties. ...more.

2018年9月8日 · Riemann zeta function for nonnegative odd integers The Riemann zeta function for odd integers has no known closed-form formula. It is not known whether those values are …

2022年6月29日 · The congruence zeta-function or the Artin–Schmidt zeta-function (see Zeta-function in algebraic geometry, below) is the analogue of Dedekind's zeta-function for fields of …

2019年9月1日 · The Riemann zeta function of 4 4 is given by: 1⋅ 082323 … 1 ⋅ 08232 3 … (−1)3B423π4 4! (− 1) 3 B 4 2 3 π 4 4! (−1)3(− 1 30) 23π4 4! (− 1) 3 (− 1 30) 2 3 π 4 4! .

2018年2月9日 · ζ(4) = 1 + 1 24 + 1 34 + … = π4 90.