Even Riemann Zeta
The Values of Riemann Zeta Function for Positive Even Integers
For any positive integer 2n,
,
where 
is a Bernoulli number [1].
is a Bernoulli number [1].
The first 33 values in closed-form of the Riemann zeta function at positive even integers are
1. 
, where 
, where
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 
, where
, where
and
32. 
, where
, where
and
33. 
, where
, where
and
(3/17/2009)
References
[1] Sury, B. Bernoulli numbers and the riemann zeta function. Reson 8, 54–62 (2003). https://doi.org/10.1007/BF02834403.
In-Text or Website Citation
Tue N. Vu, The Values of Riemann Zeta Function for Positive Even Integers, from Series Math Study Resource.
Hyperlink: http://seriesmathstudy.com/sms/evenriemannzeta.