Submitted by admin on Tue, 03/17/2009 - 3:09pm
The Values of Riemann Zeta Function for Positive Even Integers
For any positive integer 2n,

where
is a Bernoulli number [1].

The first 33 values in closed-form of the Riemann zeta function at positive even integers are
1.
, 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


and


32.
, where



and



33.
, 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.
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