Category:Riemann Zeta Function at Even Integers
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This category contains pages concerning Riemann Zeta Function at Even Integers:
The Riemann $\zeta$ function can be calculated for even integers as follows:
| \(\ds \map \zeta {2 n}\) | \(=\) | \(\ds \paren {-1}^{n + 1} \dfrac {B_{2 n} 2^{2 n - 1} \pi^{2 n} } {\paren {2 n}!}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \frac 1 {1^{2 n} } + \frac 1 {2^{2 n} } + \frac 1 {3^{2 n} } + \frac 1 {4^{2 n} } + \cdots\) |
where:
- $B_n$ are the Bernoulli numbers
- $n$ is a positive integer.
Subcategories
This category has the following 4 subcategories, out of 4 total.
B
- Basel Problem (12 P)
R
- Riemann Zeta Function of 4 (6 P)
- Riemann Zeta Function of 6 (4 P)
Pages in category "Riemann Zeta Function at Even Integers"
The following 23 pages are in this category, out of 23 total.
R
- Riemann Zeta Function at Even Integers
- Riemann Zeta Function at Even Integers/Also presented as
- Riemann Zeta Function at Even Integers/Corollary
- Riemann Zeta Function at Even Integers/Corollary/Also presented as
- Riemann Zeta Function at Even Integers/Examples
- Riemann Zeta Function at Even Integers/Examples/2
- Riemann Zeta Function at Even Integers/Examples/26
- Riemann Zeta Function at Even Integers/Examples/4
- Riemann Zeta Function at Even Integers/Examples/6
- Riemann Zeta Function at Even Integers/Examples/8
- Riemann Zeta Function at Even Integers/Lemma
- Riemann Zeta Function at Even Integers/Lemma/Proof 1
- Riemann Zeta Function at Even Integers/Lemma/Proof 2
- Riemann Zeta Function at Even Integers/Proof 2
- Riemann Zeta Function of 2
- Riemann Zeta Function of 4
- Riemann Zeta Function of 6
- Riemann Zeta Function of 8