Chú thích 1 + 2 + 3 + 4 + ⋯

  1. 1 2 3 The Euler–Maclaurin formula, Bernoulli numbers, the zeta function, and real-variable analytic continuation 
  2. ↑ Vertex operator algebras and the zeta function, 1999 
  3. ↑ Tong, David (February 23, 2012). "String Theory". p. 28–48. arΧiv:0908.0333 [hep-th]. 
  4. ↑ Moonshine Beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics, ISBN 978-0521141888 
  5. ↑ The bridge between the continuous and the discrete via original sources, ISBN 978-9185143009 
  6. ↑ Hardy p.10 (More detail on the source needed)
  7. ↑ Ramanujan's Notebooks 
  8. ↑ Toils and triumphs of Srinivasa Ramanujan, the man and the mathematician 
  9. 1 2 Ramanujan's Notebooks: Part 1 
  10. ↑ Euler, Leonhard (2006). “Translation with notes of Euler's paper: Remarks on a beautiful relation between direct as well as reciprocal power series”. The Euler Archive. Truy cập ngày 22 tháng 3 năm 2007.  Originally published as Euler, Leonhard (1768). “Remarques sur un beau rapport entre les séries des puissances tant directes que réciproques”. Mémoires de l'Académie des Sciences de Berlin 17: 83–106. 
  11. ↑ Promoting numbers to functions is identified as one of two broad classes of summation methods, including Abel and Borel summation, by Knopp, Konrad (1990) [1922]. Theory and Application of Infinite Series. Dover. tr. 475–476. ISBN 0-486-66165-2. 
  12. ↑ A Primer of Analytic Number Theory: From Pythagoras to Riemann, ISBN 0-521-81309-3 
  13. ↑ Knopp, Konrad (1990) [1922]. Theory and Application of Infinite Series. Dover. tr. 490–492. ISBN 0-486-66165-2. 
  14. ↑ Berndt et al. p.53.
  15. ↑ Hardy p.346
  16. ↑ The Casimir effect in conformal field theories 
  17. ↑ See v:Quantum mechanics/Casimir effect in one dimension
  18. ↑ Zee pp.65–67
  19. ↑ , ISBN 9783540347644  |tựa đề= trống hay bị thiếu (trợ giúp)
  20. ↑ The Indian Clerk 
  21. ↑ , ISBN 9781849432993  |tựa đề= trống hay bị thiếu (trợ giúp)
  22. ↑ In the End, It All Adds Up to –1/12 
  23. ↑ 1 + 2 + 3 + 4 + 5 +... = –1/12 Video trên YouTube
  24. ↑ of Natural Numbers (second proof and extra footage) Video trên YouTube
  25. ↑ What do we get if we sum all the natural numbers? 
  26. ↑ Schultz, Colin (31 tháng 1 năm 2014). “The Great Debate Over Whether 1+2+3+4..+ ∞ = −1/12”. Smithsonian. Truy cập ngày 16 tháng 5 năm 2016. 

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